Nothing
R/gumbelExpr.R
In copula: Multivariate Dependence with Copulas
## This file is not to be edited. It is generated by ../inst/docs/mathnb/exprPrep.R
`gumbelCopula.cdf.expr` <-
expression(E^(-((-log(u1))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)))
`gumbelCopula.cdf.algr` <-
expression({
.value <- E^-((-log(u1))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.cdfDerWrtArg.expr` <-
expression(E^(-((-log(u1))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))), E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))))
`gumbelCopula.cdfDerWrtArg.algr` <-
expression({
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.value <- E^-.expr3^.expr4 * (log(E) * (.expr3^(.expr4 -
1) * (.expr4 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr7 <- .expr2^alpha + (-log(u2))^alpha
.expr8 <- 1/alpha
.value <- E^-.expr7^.expr8 * (log(E) * (.expr7^(.expr8 -
1) * (.expr8 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr11 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha
.expr12 <- 1/alpha
.value <- E^-.expr11^.expr12 * (log(E) * (.expr11^(.expr12 -
1) * (.expr12 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr15 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha
.expr16 <- 1/alpha
.value <- E^-.expr15^.expr16 * (log(E) * (.expr15^(.expr16 -
1) * (.expr16 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr19 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha
.expr20 <- 1/alpha
.value <- E^-.expr19^.expr20 * (log(E) * (.expr19^(.expr20 -
1) * (.expr20 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr23 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha
.expr24 <- 1/alpha
.value <- E^-.expr23^.expr24 * (log(E) * (.expr23^(.expr24 -
1) * (.expr24 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr27 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha
.expr28 <- 1/alpha
.value <- E^-.expr27^.expr28 * (log(E) * (.expr27^(.expr28 -
1) * (.expr28 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr31 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha
.expr32 <- 1/alpha
.value <- E^-.expr31^.expr32 * (log(E) * (.expr31^(.expr32 -
1) * (.expr32 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr35 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha
.expr36 <- 1/alpha
.value <- E^-.expr35^.expr36 * (log(E) * (.expr35^(.expr36 -
1) * (.expr36 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr39 <- .expr2^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha
.expr40 <- 1/alpha
.value <- E^-.expr39^.expr40 * (log(E) * (.expr39^(.expr40 -
1) * (.expr40 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.cdfDerWrtPar.expr` <-
expression(-(E^(-((-log(u1))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))))) -
((-log(u1))^alpha)^(1/alpha) * (log(((-log(u1))^alpha)) *
(1/alpha^2))))), -(E^(-((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2))))), -(E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2))))),
-(E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2))))), -(E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (1/alpha^2))))), -(E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))))),
-(E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))))), -(E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))))), -(E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (1/alpha^2))))),
-(E^(-((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))))))
`gumbelCopula.cdfDerWrtPar.algr` <-
expression({
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.expr5 <- .expr3^.expr4
.value <- -(E^-.expr5 * (log(E) * (.expr3^(.expr4 - 1) *
(.expr4 * (.expr3 * log(.expr2))) - .expr5 * (log(.expr3) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr7 <- .expr3 + .expr6
.expr8 <- 1/alpha
.expr9 <- .expr7^.expr8
.value <- -(E^-.expr9 * (log(E) * (.expr7^(.expr8 - 1) *
(.expr8 * (.expr3 * log(.expr2) + .expr6 * log(.expr5))) -
.expr9 * (log(.expr7) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr11 <- .expr3 + .expr6 + .expr10
.expr12 <- 1/alpha
.expr13 <- .expr11^.expr12
.value <- -(E^-.expr13 * (log(E) * (.expr11^(.expr12 - 1) *
(.expr12 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9))) - .expr13 * (log(.expr11) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr15 <- .expr3 + .expr6 + .expr10 + .expr14
.expr16 <- 1/alpha
.expr17 <- .expr15^.expr16
.value <- -(E^-.expr17 * (log(E) * (.expr15^(.expr16 - 1) *
(.expr16 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13))) -
.expr17 * (log(.expr15) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr19 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18
.expr20 <- 1/alpha
.expr21 <- .expr19^.expr20
.value <- -(E^-.expr21 * (log(E) * (.expr19^(.expr20 - 1) *
(.expr20 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17))) - .expr21 * (log(.expr19) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr23 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22
.expr24 <- 1/alpha
.expr25 <- .expr23^.expr24
.value <- -(E^-.expr25 * (log(E) * (.expr23^(.expr24 - 1) *
(.expr24 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21))) -
.expr25 * (log(.expr23) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr25 <- -log(u7)
.expr26 <- .expr25^alpha
.expr27 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26
.expr28 <- 1/alpha
.expr29 <- .expr27^.expr28
.value <- -(E^-.expr29 * (log(E) * (.expr27^(.expr28 - 1) *
(.expr28 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25))) - .expr29 * (log(.expr27) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr25 <- -log(u7)
.expr26 <- .expr25^alpha
.expr29 <- -log(u8)
.expr30 <- .expr29^alpha
.expr31 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26 + .expr30
.expr32 <- 1/alpha
.expr33 <- .expr31^.expr32
.value <- -(E^-.expr33 * (log(E) * (.expr31^(.expr32 - 1) *
(.expr32 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25) + .expr30 * log(.expr29))) -
.expr33 * (log(.expr31) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr25 <- -log(u7)
.expr26 <- .expr25^alpha
.expr29 <- -log(u8)
.expr30 <- .expr29^alpha
.expr33 <- -log(u9)
.expr34 <- .expr33^alpha
.expr35 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26 + .expr30 + .expr34
.expr36 <- 1/alpha
.expr37 <- .expr35^.expr36
.value <- -(E^-.expr37 * (log(E) * (.expr35^(.expr36 - 1) *
(.expr36 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25) + .expr30 * log(.expr29) +
.expr34 * log(.expr33))) - .expr37 * (log(.expr35) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u10)
.expr6 <- .expr5^alpha
.expr9 <- -log(u2)
.expr10 <- .expr9^alpha
.expr13 <- -log(u3)
.expr14 <- .expr13^alpha
.expr17 <- -log(u4)
.expr18 <- .expr17^alpha
.expr21 <- -log(u5)
.expr22 <- .expr21^alpha
.expr25 <- -log(u6)
.expr26 <- .expr25^alpha
.expr29 <- -log(u7)
.expr30 <- .expr29^alpha
.expr33 <- -log(u8)
.expr34 <- .expr33^alpha
.expr37 <- -log(u9)
.expr38 <- .expr37^alpha
.expr39 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26 + .expr30 + .expr34 + .expr38
.expr40 <- 1/alpha
.expr41 <- .expr39^.expr40
.value <- -(E^-.expr41 * (log(E) * (.expr39^(.expr40 - 1) *
(.expr40 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25) + .expr30 * log(.expr29) +
.expr34 * log(.expr33) + .expr38 * log(.expr37))) -
.expr41 * (log(.expr39) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.pdf.expr` <-
expression(-(((-log(u1))^alpha)^(1/alpha)/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1))), ((-log(u1))^(-1 + alpha) * (-1 + alpha +
((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha)^(-2 + 1/alpha) * (-log(u2))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * u1 * u2), ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (1 + 2 * alpha^2 + 3 *
alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * (-log(u3))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) * u1 * u2 *
u3), ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 + 11 * alpha^2 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * (-log(u4))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4), -(((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-1 - 24 * alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) - 35 * alpha^2 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) *
(-log(u5))^(-1 + alpha))/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5)), ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 + 274 * alpha^4 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha)) + 85 * alpha^2 * (-1 + 7 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) * (-log(u6))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6), -(((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-1 -
720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(-7 + 1/alpha) * (-log(u7))^(-1 +
alpha))/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6 *
u7)), ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
(-log(u8))^(-1 + alpha))/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8), ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 118124 *
alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 67284 * alpha^5 * (-1 +
7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * (-log(u9))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9), ((-log(u1))^(-1 + alpha) *
(-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 +
alpha) * (-1 + 362880 * alpha^9 + 1026576 * alpha^8 * (-1 +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 -
3 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * (-log(u9))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
u1 * u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9))
`gumbelCopula.pdf.algr` <-
expression({
.expr1 <- log(u1)
.expr5 <- ((-.expr1)^alpha)^(1/alpha)
.value <- -(.expr5/(E^.expr5 * u1 * .expr1))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr4 <- -1 + alpha
.expr8 <- -log(u2)
.expr10 <- .expr2^alpha + .expr8^alpha
.expr11 <- 1/alpha
.expr12 <- .expr10^.expr11
.value <- .expr2^.expr4 * (.expr4 + .expr12) * .expr10^(-2 +
.expr11) * .expr8^.expr4/(E^.expr12 * u1 * u2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr18 <- -log(u3)
.expr20 <- .expr2^alpha + .expr7^alpha + .expr18^alpha
.expr21 <- 1/alpha
.expr22 <- .expr20^.expr21
.value <- .expr2^.expr4 * .expr7^.expr4 * (1 + 2 * alpha^2 +
3 * alpha * (.expr3 + .expr22) - 3 * .expr22 + .expr20^(2/alpha)) *
.expr20^(-3 + .expr21) * .expr18^.expr4/(E^.expr22 *
u1 * u2 * u3)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr25 <- -log(u4)
.expr27 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr25^alpha
.expr28 <- 1/alpha
.expr29 <- .expr27^.expr28
.expr37 <- .expr27^(2/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
(.expr3 + 6 * alpha^3 + 11 * alpha^2 * (.expr3 + .expr29) +
6 * alpha * (1 - 3 * .expr29 + .expr37) + 7 * .expr29 -
6 * .expr37 + .expr27^(3/alpha)) * .expr27^(-4 +
.expr28) * .expr25^.expr4/(E^.expr29 * u1 * u2 * u3 *
u4)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr31 <- -log(u5)
.expr33 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr31^alpha
.expr34 <- 1/alpha
.expr35 <- .expr33^.expr34
.expr44 <- .expr33^(2/alpha)
.expr54 <- .expr33^(3/alpha)
.value <- -(.expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * (.expr3 - 24 * alpha^4 - 50 * alpha^3 *
(.expr3 + .expr35) - 35 * alpha^2 * (1 - 3 * .expr35 +
.expr44) - 10 * alpha * (.expr3 + 7 * .expr35 - 6 * .expr44 +
.expr54) + 15 * .expr35 - 25 * .expr44 + 10 * .expr54 -
.expr33^(4/alpha)) * .expr33^(-5 + .expr34) * .expr31^.expr4/(E^.expr35 *
u1 * u2 * u3 * u4 * u5))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr37 <- -log(u6)
.expr39 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr37^alpha
.expr40 <- 1/alpha
.expr41 <- .expr39^.expr40
.expr50 <- .expr39^(2/alpha)
.expr61 <- .expr39^(3/alpha)
.expr73 <- .expr39^(4/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * (.expr3 + 120 * alpha^5 +
274 * alpha^4 * (.expr3 + .expr41) + 225 * alpha^3 *
(1 - 3 * .expr41 + .expr50) + 85 * alpha^2 * (.expr3 +
7 * .expr41 - 6 * .expr50 + .expr61) + 15 * alpha * (1 -
15 * .expr41 + 25 * .expr50 - 10 * .expr61 + .expr73) +
31 * .expr41 - 90 * .expr50 + 65 * .expr61 - 15 * .expr73 +
.expr39^(5/alpha)) * .expr39^(-6 + .expr40) * .expr37^.expr4/(E^.expr41 *
u1 * u2 * u3 * u4 * u5 * u6)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr23 <- -log(u6)
.expr43 <- -log(u7)
.expr45 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr43^alpha
.expr46 <- 1/alpha
.expr47 <- .expr45^.expr46
.expr56 <- .expr45^(2/alpha)
.expr67 <- .expr45^(3/alpha)
.expr80 <- .expr45^(4/alpha)
.expr94 <- .expr45^(5/alpha)
.value <- -(.expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * (.expr3 -
720 * alpha^6 - 1764 * alpha^5 * (.expr3 + .expr47) -
1624 * alpha^4 * (1 - 3 * .expr47 + .expr56) - 735 *
alpha^3 * (.expr3 + 7 * .expr47 - 6 * .expr56 + .expr67) -
175 * alpha^2 * (1 - 15 * .expr47 + 25 * .expr56 - 10 *
.expr67 + .expr80) - 21 * alpha * (.expr3 + 31 *
.expr47 - 90 * .expr56 + 65 * .expr67 - 15 * .expr80 +
.expr94) + 63 * .expr47 - 301 * .expr56 + 350 * .expr67 -
140 * .expr80 + 21 * .expr94 - .expr45^(6/alpha)) * .expr45^(-7 +
.expr46) * .expr43^.expr4/(E^.expr47 * u1 * u2 * u3 *
u4 * u5 * u6 * u7))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr23 <- -log(u6)
.expr27 <- -log(u7)
.expr49 <- -log(u8)
.expr51 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr49^alpha
.expr52 <- 1/alpha
.expr53 <- .expr51^.expr52
.expr62 <- .expr51^(2/alpha)
.expr73 <- .expr51^(3/alpha)
.expr86 <- .expr51^(4/alpha)
.expr101 <- .expr51^(5/alpha)
.expr117 <- .expr51^(6/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * .expr27^.expr4 *
(.expr3 + 5040 * alpha^7 + 13068 * alpha^6 * (.expr3 +
.expr53) + 13132 * alpha^5 * (1 - 3 * .expr53 + .expr62) +
6769 * alpha^4 * (.expr3 + 7 * .expr53 - 6 * .expr62 +
.expr73) + 1960 * alpha^3 * (1 - 15 * .expr53 +
25 * .expr62 - 10 * .expr73 + .expr86) + 322 * alpha^2 *
(.expr3 + 31 * .expr53 - 90 * .expr62 + 65 * .expr73 -
15 * .expr86 + .expr101) + 28 * alpha * (1 -
63 * .expr53 + 301 * .expr62 - 350 * .expr73 + 140 *
.expr86 - 21 * .expr101 + .expr117) + 127 * .expr53 -
966 * .expr62 + 1701 * .expr73 - 1050 * .expr86 +
266 * .expr101 - 28 * .expr117 + .expr51^(7/alpha)) *
.expr51^(-8 + .expr52) * .expr49^.expr4/(E^.expr53 *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr23 <- -log(u6)
.expr27 <- -log(u7)
.expr31 <- -log(u8)
.expr55 <- -log(u9)
.expr57 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr55^alpha
.expr58 <- 1/alpha
.expr59 <- .expr57^.expr58
.expr68 <- .expr57^(2/alpha)
.expr79 <- .expr57^(3/alpha)
.expr92 <- .expr57^(4/alpha)
.expr107 <- .expr57^(5/alpha)
.expr124 <- .expr57^(6/alpha)
.expr142 <- .expr57^(7/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * .expr27^.expr4 *
.expr31^.expr4 * (1 + 40320 * alpha^8 + 109584 * alpha^7 *
(.expr3 + .expr59) + 118124 * alpha^6 * (1 - 3 * .expr59 +
.expr68) + 67284 * alpha^5 * (.expr3 + 7 * .expr59 -
6 * .expr68 + .expr79) + 22449 * alpha^4 * (1 - 15 *
.expr59 + 25 * .expr68 - 10 * .expr79 + .expr92) + 4536 *
alpha^3 * (.expr3 + 31 * .expr59 - 90 * .expr68 + 65 *
.expr79 - 15 * .expr92 + .expr107) + 546 * alpha^2 *
(1 - 63 * .expr59 + 301 * .expr68 - 350 * .expr79 + 140 *
.expr92 - 21 * .expr107 + .expr124) + 36 * alpha *
(.expr3 + 127 * .expr59 - 966 * .expr68 + 1701 * .expr79 -
1050 * .expr92 + 266 * .expr107 - 28 * .expr124 +
.expr142) - 255 * .expr59 + 3025 * .expr68 - 7770 *
.expr79 + 6951 * .expr92 - 2646 * .expr107 + 462 * .expr124 -
36 * .expr142 + .expr57^(8/alpha)) * .expr57^(-9 + .expr58) *
.expr55^.expr4/(E^.expr59 * u1 * u2 * u3 * u4 * u5 *
u6 * u7 * u8 * u9)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u10)
.expr11 <- -log(u2)
.expr15 <- -log(u3)
.expr19 <- -log(u4)
.expr23 <- -log(u5)
.expr27 <- -log(u6)
.expr31 <- -log(u7)
.expr35 <- -log(u8)
.expr61 <- -log(u9)
.expr63 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr35^alpha + .expr61^alpha
.expr64 <- 1/alpha
.expr65 <- .expr63^.expr64
.expr74 <- .expr63^(2/alpha)
.expr85 <- .expr63^(3/alpha)
.expr98 <- .expr63^(4/alpha)
.expr113 <- .expr63^(5/alpha)
.expr130 <- .expr63^(6/alpha)
.expr149 <- .expr63^(7/alpha)
.expr169 <- .expr63^(8/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * .expr27^.expr4 *
.expr31^.expr4 * .expr35^.expr4 * (.expr3 + 362880 *
alpha^9 + 1026576 * alpha^8 * (.expr3 + .expr65) + 1172700 *
alpha^7 * (1 - 3 * .expr65 + .expr74) + 723680 * alpha^6 *
(.expr3 + 7 * .expr65 - 6 * .expr74 + .expr85) + 269325 *
alpha^5 * (1 - 15 * .expr65 + 25 * .expr74 - 10 * .expr85 +
.expr98) + 63273 * alpha^4 * (.expr3 + 31 * .expr65 -
90 * .expr74 + 65 * .expr85 - 15 * .expr98 + .expr113) +
9450 * alpha^3 * (1 - 63 * .expr65 + 301 * .expr74 -
350 * .expr85 + 140 * .expr98 - 21 * .expr113 + .expr130) +
870 * alpha^2 * (.expr3 + 127 * .expr65 - 966 * .expr74 +
1701 * .expr85 - 1050 * .expr98 + 266 * .expr113 -
28 * .expr130 + .expr149) + 45 * alpha * (1 - 255 *
.expr65 + 3025 * .expr74 - 7770 * .expr85 + 6951 * .expr98 -
2646 * .expr113 + 462 * .expr130 - 36 * .expr149 + .expr169) +
511 * .expr65 - 9330 * .expr74 + 34105 * .expr85 - 42525 *
.expr98 + 22827 * .expr113 - 5880 * .expr130 + 750 *
.expr149 - 45 * .expr169 + .expr63^(9/alpha)) * .expr63^(-10 +
.expr64) * .expr61^.expr4/(E^.expr65 * u1 * u10 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.pdfDerWrtArg.expr` <-
expression(((-log(u1))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1)) + ((-log(u1))^alpha)^(1/alpha) * ((E^((-log(u1))^alpha)^(1/alpha) -
E^((-log(u1))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * log(u1) + E^((-log(u1))^alpha)^(1/alpha) *
u1 * (1/u1))/(E^((-log(u1))^alpha)^(1/alpha) * u1 * log(u1))^2,
-(((-log(u1))^(-1 + alpha) * (-1 + alpha + ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)) * (((-log(u1))^alpha + (-log(u2))^alpha)^((-2 +
1/alpha) - 1) * ((-2 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + ((-log(u1))^(-1 + alpha) *
(((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
(-log(u1))^((-1 + alpha) - 1) * ((-1 + alpha) * (1/u1)) *
(-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha)^(-2 + 1/alpha)) *
(-log(u2))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
u1 * u2) + ((-log(u1))^(-1 + alpha) * (-1 + alpha + ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha)^(-2 +
1/alpha) * (-log(u2))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) - E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2)/(E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
u1 * u2)^2), -(((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((-3 +
1/alpha) - 1) * ((-3 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))) + (3 * alpha * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
3 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (1 + 2 *
alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha))) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(-3 + 1/alpha)) *
(-log(u3))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * u1 * u2 * u3) + ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (1 + 2 * alpha^2 +
3 * alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(-3 + 1/alpha) *
(-log(u3))^(-1 + alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) - E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * u1 * u2 * u3)^2), (((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(6 * alpha * (3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 11 * alpha^2 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(-4 + 1/alpha) - (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((-4 + 1/alpha) - 1) * ((-4 + 1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
(-log(u4))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 +
11 * alpha^2 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(-4 + 1/alpha) * (-log(u4))^(-1 +
alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3 * u4)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4)^2, -((((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(50 * alpha^3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 35 * alpha^2 * (3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 10 *
alpha * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 -
50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) -
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 -
50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((-5 + 1/alpha) -
1) * ((-5 + 1/alpha) * ((-log(u1))^(alpha - 1) *
(alpha * (1/u1)))))) * (-log(u5))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5) -
((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-1 - 24 * alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) - 35 * alpha^2 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) *
(-log(u5))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3 * u4 * u5)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5)^2), (((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (225 * alpha^3 * (3 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 274 * alpha^4 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
85 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))) + (7 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
15 * alpha * (15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 25 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 90 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) - 1) *
((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
65 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - (-log(u1))^((-1 + alpha) -
1) * ((-1 + alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-1 + 120 * alpha^5 + 274 * alpha^4 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 + 274 *
alpha^4 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((-6 +
1/alpha) - 1) * ((-6 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))))) * (-log(u6))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 +
274 * alpha^4 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) * (-log(u6))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2 * u3 * u4 * u5 * u6)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6)^2, -((((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(1764 * alpha^5 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 1624 * alpha^4 * (3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 735 * alpha^3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) - 175 * alpha^2 * (15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 21 * alpha * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) - 63 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 301 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 350 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 140 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 21 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-1 - 720 * alpha^6 - 1764 *
alpha^5 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) - 1624 *
alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha))) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(-7 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-1 -
720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) - 175 * alpha^2 *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha)) -
21 * alpha * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(6/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((-7 + 1/alpha) - 1) * ((-7 + 1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
(-log(u7))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6 * u7) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-1 - 720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha *
(-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(6/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(-7 + 1/alpha) * (-log(u7))^(-1 +
alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3 * u4 * u5 * u6 * u7)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7)^2), (((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (13132 * alpha^5 *
(3 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 13068 * alpha^6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 6769 * alpha^4 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 1960 * alpha^3 * (15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 25 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 10 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 322 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 28 * alpha * (63 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 301 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 350 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 140 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 21 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 127 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 966 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 1701 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 1050 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 266 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 28 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((7/alpha) - 1) *
((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
(-log(u1))^((-1 + alpha) - 1) * ((-1 + alpha) * (1/u1)) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha)) + 1960 * alpha^3 *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha)) + 28 * alpha *
(1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) -
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-1 + 5040 * alpha^7 + 13068 * alpha^6 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) +
13132 * alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((-8 + 1/alpha) -
1) * ((-8 + 1/alpha) * ((-log(u1))^(alpha - 1) *
(alpha * (1/u1)))))) * (-log(u8))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 *
u6 * u7 * u8) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) +
13132 * alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
(-log(u8))^(-1 + alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2 * u3 * u4 * u5 * u6 *
u7 * u8)/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6 * u7 * u8)^2, (((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(118124 * alpha^6 * (3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 109584 * alpha^7 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 67284 * alpha^5 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 6 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 22449 * alpha^4 * (15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 10 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 4536 *
alpha^3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))) + (65 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 90 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
546 * alpha^2 * (63 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
301 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
350 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
140 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
21 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) *
(alpha * (1/u1))))) - 36 * alpha * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (266 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + (1701 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (127 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 966 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 1050 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
28 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 255 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 3025 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 7770 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 6951 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 2646 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 462 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 36 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((7/alpha) - 1) * ((7/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) -
1) * ((8/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 +
alpha) * (1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
118124 * alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (1 + 40320 * alpha^8 +
109584 * alpha^7 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 118124 * alpha^6 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((-9 +
1/alpha) - 1) * ((-9 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))))) * (-log(u9))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
118124 * alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * (-log(u9))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2 * u3 * u4 * u5 * u6 * u7 *
u8 * u9)/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)^2, (((-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (1172700 * alpha^7 *
(3 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 1026576 * alpha^8 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 723680 * alpha^6 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
6 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
269325 * alpha^5 * (15 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 25 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 10 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 63273 * alpha^4 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (65 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
(31 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 90 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
15 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
9450 * alpha^3 * (63 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 301 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 350 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 140 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 21 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 870 * alpha^2 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (266 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) - 1) *
((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
(1701 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + (127 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
966 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
1050 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
28 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
45 * alpha * (255 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 3025 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 7770 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6951 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 2646 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 462 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 36 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) -
1) * ((8/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 511 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
9330 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 34105 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 42525 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 22827 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 5880 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 750 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((7/alpha) - 1) * ((7/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 45 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((8/alpha) - 1) * ((8/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((9/alpha) -
1) * ((9/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 + alpha) *
(1/u1)) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 +
1026576 * alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
1172700 * alpha^7 * (1 - 3 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 723680 * alpha^6 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 *
(1 - 15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
63273 * alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
9450 * alpha^3 * (1 - 63 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 350 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) - 21 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) +
511 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 9330 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
34105 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 42525 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
22827 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 5880 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
750 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) - 45 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(9/alpha))) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(-1 + 362880 * alpha^9 + 1026576 * alpha^8 * (-1 + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
1172700 * alpha^7 * (1 - 3 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 723680 * alpha^6 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
269325 * alpha^5 * (1 - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 63273 * alpha^4 *
(-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 *
(1 - 63 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha *
(1 - 255 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((-10 + 1/alpha) - 1) * ((-10 +
1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
(-log(u9))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 *
u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 +
1026576 * alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
1172700 * alpha^7 * (1 - 3 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 723680 * alpha^6 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 *
(1 - 15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
63273 * alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
9450 * alpha^3 * (1 - 63 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 350 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) - 21 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) +
511 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 9330 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
34105 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 42525 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
22827 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 5880 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
750 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) - 45 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * (-log(u9))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
E^((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9)/(E^((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 *
u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)^2)
`gumbelCopula.pdfDerWrtArg.algr` <-
expression({
.expr1 <- log(u1)
.expr2 <- -.expr1
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.expr9 <- 1/u1
.expr13 <- .expr3^(.expr4 - 1) * (.expr4 * (.expr2^(alpha -
1) * (alpha * .expr9)))
.expr14 <- .expr3^.expr4
.expr15 <- E^.expr14
.expr16 <- .expr15 * u1
.expr17 <- .expr16 * .expr1
.value <- .expr13/.expr17 + .expr14 * ((.expr15 - .expr15 *
(log(E) * .expr13) * u1) * .expr1 + .expr16 * .expr9)/.expr17^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr4 <- -1 + alpha
.expr5 <- .expr2^.expr4
.expr8 <- -log(u2)
.expr10 <- .expr2^alpha + .expr8^alpha
.expr11 <- 1/alpha
.expr12 <- .expr10^.expr11
.expr13 <- .expr4 + .expr12
.expr14 <- .expr5 * .expr13
.expr16 <- -2 + .expr11
.expr21 <- 1/u1
.expr23 <- .expr2^(alpha - 1) * (alpha * .expr21)
.expr30 <- .expr10^(.expr11 - 1) * (.expr11 * .expr23)
.expr38 <- .expr10^.expr16
.expr41 <- .expr8^.expr4
.expr43 <- E^.expr12
.expr45 <- .expr43 * u1 * u2
.value <- -((.expr14 * (.expr10^(.expr16 - 1) * (.expr16 *
.expr23)) + (.expr5 * .expr30 + .expr2^(.expr4 - 1) *
(.expr4 * .expr21) * .expr13) * .expr38) * .expr41/.expr45 +
.expr14 * .expr38 * .expr41 * ((.expr43 - .expr43 * (log(E) *
.expr30) * u1) * u2)/.expr45^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr9 <- .expr2^.expr4 * .expr8
.expr13 <- 3 * alpha
.expr18 <- -log(u3)
.expr20 <- .expr2^alpha + .expr7^alpha + .expr18^alpha
.expr21 <- 1/alpha
.expr22 <- .expr20^.expr21
.expr28 <- 2/alpha
.expr30 <- 1 + 2 * alpha^2 + .expr13 * (.expr3 + .expr22) -
3 * .expr22 + .expr20^.expr28
.expr31 <- .expr9 * .expr30
.expr33 <- -3 + .expr21
.expr38 <- 1/u1
.expr40 <- .expr2^(alpha - 1) * (alpha * .expr38)
.expr51 <- .expr20^(.expr21 - 1) * (.expr21 * .expr40)
.expr64 <- .expr20^.expr33
.expr67 <- .expr18^.expr4
.expr69 <- E^.expr22
.expr72 <- .expr69 * u1 * u2 * u3
.value <- -((.expr31 * (.expr20^(.expr33 - 1) * (.expr33 *
.expr40)) + (.expr9 * (.expr20^(.expr28 - 1) * (.expr28 *
.expr40) + (.expr13 * .expr51 - 3 * .expr51)) + .expr2^(.expr4 -
1) * (.expr4 * .expr38) * .expr8 * .expr30) * .expr64) *
.expr67/.expr72 + .expr31 * .expr64 * .expr67 * ((.expr69 -
.expr69 * (log(E) * .expr51) * u1) * u2 * u3)/.expr72^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr13 <- .expr2^.expr4 * .expr8 * .expr12
.expr14 <- 6 * alpha
.expr21 <- -log(u4)
.expr23 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr21^alpha
.expr24 <- 1/alpha
.expr29 <- 1/u1
.expr31 <- .expr2^(alpha - 1) * (alpha * .expr29)
.expr33 <- .expr23^(.expr24 - 1) * (.expr24 * .expr31)
.expr35 <- 2/alpha
.expr39 <- .expr23^(.expr35 - 1) * (.expr35 * .expr31)
.expr43 <- 11 * alpha^2
.expr50 <- 3/alpha
.expr66 <- .expr23^.expr24
.expr72 <- .expr23^.expr35
.expr81 <- .expr3 + 6 * alpha^3 + .expr43 * (.expr3 + .expr66) +
.expr14 * (1 - 3 * .expr66 + .expr72) + 7 * .expr66 -
6 * .expr72 + .expr23^.expr50
.expr85 <- -4 + .expr24
.expr86 <- .expr23^.expr85
.expr88 <- .expr13 * .expr81
.expr95 <- .expr21^.expr4
.expr97 <- E^.expr66
.expr101 <- .expr97 * u1 * u2 * u3 * u4
.value <- ((.expr13 * (.expr14 * (3 * .expr33 - .expr39) -
.expr43 * .expr33 - 7 * .expr33 + 6 * .expr39 - .expr23^(.expr50 -
1) * (.expr50 * .expr31)) - .expr2^(.expr4 - 1) * (.expr4 *
.expr29) * .expr8 * .expr12 * .expr81) * .expr86 - .expr88 *
(.expr23^(.expr85 - 1) * (.expr85 * .expr31))) * .expr95/.expr101 -
.expr88 * .expr86 * .expr95 * ((.expr97 - .expr97 * (log(E) *
.expr33) * u1) * u2 * u3 * u4)/.expr101^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr17 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16
.expr19 <- 50 * alpha^3
.expr28 <- -log(u5)
.expr30 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr28^alpha
.expr31 <- 1/alpha
.expr36 <- 1/u1
.expr38 <- .expr2^(alpha - 1) * (alpha * .expr36)
.expr40 <- .expr30^(.expr31 - 1) * (.expr31 * .expr38)
.expr43 <- 35 * alpha^2
.expr45 <- 2/alpha
.expr49 <- .expr30^(.expr45 - 1) * (.expr45 * .expr38)
.expr53 <- 10 * alpha
.expr54 <- 3/alpha
.expr58 <- .expr30^(.expr54 - 1) * (.expr54 * .expr38)
.expr71 <- 4/alpha
.expr88 <- .expr30^.expr31
.expr94 <- .expr30^.expr45
.expr102 <- .expr30^.expr54
.expr113 <- .expr3 - 24 * alpha^4 - .expr19 * (.expr3 + .expr88) -
.expr43 * (1 - 3 * .expr88 + .expr94) - .expr53 * (.expr3 +
7 * .expr88 - 6 * .expr94 + .expr102) + 15 * .expr88 -
25 * .expr94 + 10 * .expr102 - .expr30^.expr71
.expr117 <- -5 + .expr31
.expr118 <- .expr30^.expr117
.expr120 <- .expr17 * .expr113
.expr127 <- .expr28^.expr4
.expr129 <- E^.expr88
.expr134 <- .expr129 * u1 * u2 * u3 * u4 * u5
.value <- -(((.expr17 * (.expr19 * .expr40 - .expr43 * (3 *
.expr40 - .expr49) + .expr53 * (.expr58 + (7 * .expr40 -
6 * .expr49)) - 15 * .expr40 + 25 * .expr49 - 10 * .expr58 +
.expr30^(.expr71 - 1) * (.expr71 * .expr38)) - .expr2^(.expr4 -
1) * (.expr4 * .expr36) * .expr8 * .expr12 * .expr16 *
.expr113) * .expr118 - .expr120 * (.expr30^(.expr117 -
1) * (.expr117 * .expr38))) * .expr127/.expr134 - .expr120 *
.expr118 * .expr127 * ((.expr129 - .expr129 * (log(E) *
.expr40) * u1) * u2 * u3 * u4 * u5)/.expr134^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr21 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20
.expr23 <- 225 * alpha^3
.expr34 <- -log(u6)
.expr36 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr34^alpha
.expr37 <- 1/alpha
.expr42 <- 1/u1
.expr44 <- .expr2^(alpha - 1) * (alpha * .expr42)
.expr46 <- .expr36^(.expr37 - 1) * (.expr37 * .expr44)
.expr48 <- 2/alpha
.expr52 <- .expr36^(.expr48 - 1) * (.expr48 * .expr44)
.expr56 <- 274 * alpha^4
.expr60 <- 85 * alpha^2
.expr61 <- 3/alpha
.expr65 <- .expr36^(.expr61 - 1) * (.expr61 * .expr44)
.expr72 <- 15 * alpha
.expr78 <- 4/alpha
.expr82 <- .expr36^(.expr78 - 1) * (.expr78 * .expr44)
.expr94 <- 5/alpha
.expr112 <- .expr36^.expr37
.expr118 <- .expr36^.expr48
.expr126 <- .expr36^.expr61
.expr136 <- .expr36^.expr78
.expr149 <- .expr3 + 120 * alpha^5 + .expr56 * (.expr3 +
.expr112) + .expr23 * (1 - 3 * .expr112 + .expr118) +
.expr60 * (.expr3 + 7 * .expr112 - 6 * .expr118 + .expr126) +
.expr72 * (1 - 15 * .expr112 + 25 * .expr118 - 10 * .expr126 +
.expr136) + 31 * .expr112 - 90 * .expr118 + 65 *
.expr126 - 15 * .expr136 + .expr36^.expr94
.expr153 <- -6 + .expr37
.expr154 <- .expr36^.expr153
.expr156 <- .expr21 * .expr149
.expr163 <- .expr34^.expr4
.expr165 <- E^.expr112
.expr171 <- .expr165 * u1 * u2 * u3 * u4 * u5 * u6
.value <- ((.expr21 * (.expr23 * (3 * .expr46 - .expr52) -
.expr56 * .expr46 - .expr60 * (.expr65 + (7 * .expr46 -
6 * .expr52)) + .expr72 * (15 * .expr46 - 25 * .expr52 +
10 * .expr65 - .expr82) - 31 * .expr46 + 90 * .expr52 -
65 * .expr65 + 15 * .expr82 - .expr36^(.expr94 - 1) *
(.expr94 * .expr44)) - .expr2^(.expr4 - 1) * (.expr4 *
.expr42) * .expr8 * .expr12 * .expr16 * .expr20 * .expr149) *
.expr154 - .expr156 * (.expr36^(.expr153 - 1) * (.expr153 *
.expr44))) * .expr163/.expr171 - .expr156 * .expr154 *
.expr163 * ((.expr165 - .expr165 * (log(E) * .expr46) *
u1) * u2 * u3 * u4 * u5 * u6)/.expr171^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u6)
.expr24 <- .expr23^.expr4
.expr25 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24
.expr27 <- 1764 * alpha^5
.expr40 <- -log(u7)
.expr42 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr40^alpha
.expr43 <- 1/alpha
.expr48 <- 1/u1
.expr50 <- .expr2^(alpha - 1) * (alpha * .expr48)
.expr52 <- .expr42^(.expr43 - 1) * (.expr43 * .expr50)
.expr55 <- 1624 * alpha^4
.expr57 <- 2/alpha
.expr61 <- .expr42^(.expr57 - 1) * (.expr57 * .expr50)
.expr66 <- 735 * alpha^3
.expr67 <- 3/alpha
.expr71 <- .expr42^(.expr67 - 1) * (.expr67 * .expr50)
.expr79 <- 175 * alpha^2
.expr85 <- 4/alpha
.expr89 <- .expr42^(.expr85 - 1) * (.expr85 * .expr50)
.expr93 <- 21 * alpha
.expr94 <- 5/alpha
.expr98 <- .expr42^(.expr94 - 1) * (.expr94 * .expr50)
.expr119 <- 6/alpha
.expr138 <- .expr42^.expr43
.expr144 <- .expr42^.expr57
.expr152 <- .expr42^.expr67
.expr162 <- .expr42^.expr85
.expr174 <- .expr42^.expr94
.expr189 <- .expr3 - 720 * alpha^6 - .expr27 * (.expr3 +
.expr138) - .expr55 * (1 - 3 * .expr138 + .expr144) -
.expr66 * (.expr3 + 7 * .expr138 - 6 * .expr144 + .expr152) -
.expr79 * (1 - 15 * .expr138 + 25 * .expr144 - 10 * .expr152 +
.expr162) - .expr93 * (.expr3 + 31 * .expr138 - 90 *
.expr144 + 65 * .expr152 - 15 * .expr162 + .expr174) +
63 * .expr138 - 301 * .expr144 + 350 * .expr152 - 140 *
.expr162 + 21 * .expr174 - .expr42^.expr119
.expr193 <- -7 + .expr43
.expr194 <- .expr42^.expr193
.expr196 <- .expr25 * .expr189
.expr203 <- .expr40^.expr4
.expr205 <- E^.expr138
.expr212 <- .expr205 * u1 * u2 * u3 * u4 * u5 * u6 * u7
.value <- -(((.expr25 * (.expr27 * .expr52 - .expr55 * (3 *
.expr52 - .expr61) + .expr66 * (.expr71 + (7 * .expr52 -
6 * .expr61)) - .expr79 * (15 * .expr52 - 25 * .expr61 +
10 * .expr71 - .expr89) + .expr93 * (.expr98 + (65 *
.expr71 + (31 * .expr52 - 90 * .expr61) - 15 * .expr89)) -
63 * .expr52 + 301 * .expr61 - 350 * .expr71 + 140 *
.expr89 - 21 * .expr98 + .expr42^(.expr119 - 1) * (.expr119 *
.expr50)) - .expr2^(.expr4 - 1) * (.expr4 * .expr48) *
.expr8 * .expr12 * .expr16 * .expr20 * .expr24 * .expr189) *
.expr194 - .expr196 * (.expr42^(.expr193 - 1) * (.expr193 *
.expr50))) * .expr203/.expr212 - .expr196 * .expr194 *
.expr203 * ((.expr205 - .expr205 * (log(E) * .expr52) *
u1) * u2 * u3 * u4 * u5 * u6 * u7)/.expr212^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u6)
.expr24 <- .expr23^.expr4
.expr27 <- -log(u7)
.expr28 <- .expr27^.expr4
.expr29 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24 * .expr28
.expr31 <- 13132 * alpha^5
.expr46 <- -log(u8)
.expr48 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr46^alpha
.expr49 <- 1/alpha
.expr54 <- 1/u1
.expr56 <- .expr2^(alpha - 1) * (alpha * .expr54)
.expr58 <- .expr48^(.expr49 - 1) * (.expr49 * .expr56)
.expr60 <- 2/alpha
.expr64 <- .expr48^(.expr60 - 1) * (.expr60 * .expr56)
.expr68 <- 13068 * alpha^6
.expr72 <- 6769 * alpha^4
.expr73 <- 3/alpha
.expr77 <- .expr48^(.expr73 - 1) * (.expr73 * .expr56)
.expr85 <- 1960 * alpha^3
.expr91 <- 4/alpha
.expr95 <- .expr48^(.expr91 - 1) * (.expr91 * .expr56)
.expr100 <- 322 * alpha^2
.expr101 <- 5/alpha
.expr105 <- .expr48^(.expr101 - 1) * (.expr101 * .expr56)
.expr116 <- 28 * alpha
.expr126 <- 6/alpha
.expr130 <- .expr48^(.expr126 - 1) * (.expr126 * .expr56)
.expr146 <- 7/alpha
.expr166 <- .expr48^.expr49
.expr172 <- .expr48^.expr60
.expr180 <- .expr48^.expr73
.expr190 <- .expr48^.expr91
.expr202 <- .expr48^.expr101
.expr216 <- .expr48^.expr126
.expr233 <- .expr3 + 5040 * alpha^7 + .expr68 * (.expr3 +
.expr166) + .expr31 * (1 - 3 * .expr166 + .expr172) +
.expr72 * (.expr3 + 7 * .expr166 - 6 * .expr172 + .expr180) +
.expr85 * (1 - 15 * .expr166 + 25 * .expr172 - 10 * .expr180 +
.expr190) + .expr100 * (.expr3 + 31 * .expr166 -
90 * .expr172 + 65 * .expr180 - 15 * .expr190 + .expr202) +
.expr116 * (1 - 63 * .expr166 + 301 * .expr172 - 350 *
.expr180 + 140 * .expr190 - 21 * .expr202 + .expr216) +
127 * .expr166 - 966 * .expr172 + 1701 * .expr180 - 1050 *
.expr190 + 266 * .expr202 - 28 * .expr216 + .expr48^.expr146
.expr237 <- -8 + .expr49
.expr238 <- .expr48^.expr237
.expr240 <- .expr29 * .expr233
.expr247 <- .expr46^.expr4
.expr249 <- E^.expr166
.expr257 <- .expr249 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8
.value <- ((.expr29 * (.expr31 * (3 * .expr58 - .expr64) -
.expr68 * .expr58 - .expr72 * (.expr77 + (7 * .expr58 -
6 * .expr64)) + .expr85 * (15 * .expr58 - 25 * .expr64 +
10 * .expr77 - .expr95) - .expr100 * (.expr105 + (65 *
.expr77 + (31 * .expr58 - 90 * .expr64) - 15 * .expr95)) +
.expr116 * (63 * .expr58 - 301 * .expr64 + 350 * .expr77 -
140 * .expr95 + 21 * .expr105 - .expr130) - 127 *
.expr58 + 966 * .expr64 - 1701 * .expr77 + 1050 * .expr95 -
266 * .expr105 + 28 * .expr130 - .expr48^(.expr146 -
1) * (.expr146 * .expr56)) - .expr2^(.expr4 - 1) * (.expr4 *
.expr54) * .expr8 * .expr12 * .expr16 * .expr20 * .expr24 *
.expr28 * .expr233) * .expr238 - .expr240 * (.expr48^(.expr237 -
1) * (.expr237 * .expr56))) * .expr247/.expr257 - .expr240 *
.expr238 * .expr247 * ((.expr249 - .expr249 * (log(E) *
.expr58) * u1) * u2 * u3 * u4 * u5 * u6 * u7 * u8)/.expr257^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u6)
.expr24 <- .expr23^.expr4
.expr27 <- -log(u7)
.expr28 <- .expr27^.expr4
.expr31 <- -log(u8)
.expr32 <- .expr31^.expr4
.expr33 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24 * .expr28 * .expr32
.expr35 <- 118124 * alpha^6
.expr52 <- -log(u9)
.expr54 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr52^alpha
.expr55 <- 1/alpha
.expr60 <- 1/u1
.expr62 <- .expr2^(alpha - 1) * (alpha * .expr60)
.expr64 <- .expr54^(.expr55 - 1) * (.expr55 * .expr62)
.expr66 <- 2/alpha
.expr70 <- .expr54^(.expr66 - 1) * (.expr66 * .expr62)
.expr74 <- 109584 * alpha^7
.expr78 <- 67284 * alpha^5
.expr79 <- 3/alpha
.expr83 <- .expr54^(.expr79 - 1) * (.expr79 * .expr62)
.expr91 <- 22449 * alpha^4
.expr97 <- 4/alpha
.expr101 <- .expr54^(.expr97 - 1) * (.expr97 * .expr62)
.expr106 <- 4536 * alpha^3
.expr107 <- 5/alpha
.expr111 <- .expr54^(.expr107 - 1) * (.expr107 * .expr62)
.expr123 <- 546 * alpha^2
.expr133 <- 6/alpha
.expr137 <- .expr54^(.expr133 - 1) * (.expr133 * .expr62)
.expr141 <- 36 * alpha
.expr142 <- 7/alpha
.expr146 <- .expr54^(.expr142 - 1) * (.expr142 * .expr62)
.expr175 <- 8/alpha
.expr196 <- .expr54^.expr55
.expr202 <- .expr54^.expr66
.expr210 <- .expr54^.expr79
.expr220 <- .expr54^.expr97
.expr232 <- .expr54^.expr107
.expr246 <- .expr54^.expr133
.expr262 <- .expr54^.expr142
.expr281 <- 1 + 40320 * alpha^8 + .expr74 * (.expr3 + .expr196) +
.expr35 * (1 - 3 * .expr196 + .expr202) + .expr78 * (.expr3 +
7 * .expr196 - 6 * .expr202 + .expr210) + .expr91 * (1 -
15 * .expr196 + 25 * .expr202 - 10 * .expr210 + .expr220) +
.expr106 * (.expr3 + 31 * .expr196 - 90 * .expr202 +
65 * .expr210 - 15 * .expr220 + .expr232) + .expr123 *
(1 - 63 * .expr196 + 301 * .expr202 - 350 * .expr210 +
140 * .expr220 - 21 * .expr232 + .expr246) + .expr141 *
(.expr3 + 127 * .expr196 - 966 * .expr202 + 1701 * .expr210 -
1050 * .expr220 + 266 * .expr232 - 28 * .expr246 +
.expr262) - 255 * .expr196 + 3025 * .expr202 - 7770 *
.expr210 + 6951 * .expr220 - 2646 * .expr232 + 462 *
.expr246 - 36 * .expr262 + .expr54^.expr175
.expr285 <- -9 + .expr55
.expr286 <- .expr54^.expr285
.expr288 <- .expr33 * .expr281
.expr295 <- .expr52^.expr4
.expr297 <- E^.expr196
.expr306 <- .expr297 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8 * u9
.value <- ((.expr33 * (.expr35 * (3 * .expr64 - .expr70) -
.expr74 * .expr64 - .expr78 * (.expr83 + (7 * .expr64 -
6 * .expr70)) + .expr91 * (15 * .expr64 - 25 * .expr70 +
10 * .expr83 - .expr101) - .expr106 * (.expr111 + (65 *
.expr83 + (31 * .expr64 - 90 * .expr70) - 15 * .expr101)) +
.expr123 * (63 * .expr64 - 301 * .expr70 + 350 * .expr83 -
140 * .expr101 + 21 * .expr111 - .expr137) - .expr141 *
(.expr146 + (266 * .expr111 + (1701 * .expr83 + (127 *
.expr64 - 966 * .expr70) - 1050 * .expr101) - 28 *
.expr137)) + 255 * .expr64 - 3025 * .expr70 + 7770 *
.expr83 - 6951 * .expr101 + 2646 * .expr111 - 462 * .expr137 +
36 * .expr146 - .expr54^(.expr175 - 1) * (.expr175 *
.expr62)) - .expr2^(.expr4 - 1) * (.expr4 * .expr60) *
.expr8 * .expr12 * .expr16 * .expr20 * .expr24 * .expr28 *
.expr32 * .expr281) * .expr286 - .expr288 * (.expr54^(.expr285 -
1) * (.expr285 * .expr62))) * .expr295/.expr306 - .expr288 *
.expr286 * .expr295 * ((.expr297 - .expr297 * (log(E) *
.expr64) * u1) * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)/.expr306^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u10)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u2)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u3)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u4)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u5)
.expr24 <- .expr23^.expr4
.expr27 <- -log(u6)
.expr28 <- .expr27^.expr4
.expr31 <- -log(u7)
.expr32 <- .expr31^.expr4
.expr35 <- -log(u8)
.expr36 <- .expr35^.expr4
.expr37 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24 * .expr28 * .expr32 * .expr36
.expr39 <- 1172700 * alpha^7
.expr58 <- -log(u9)
.expr60 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr35^alpha + .expr58^alpha
.expr61 <- 1/alpha
.expr66 <- 1/u1
.expr68 <- .expr2^(alpha - 1) * (alpha * .expr66)
.expr70 <- .expr60^(.expr61 - 1) * (.expr61 * .expr68)
.expr72 <- 2/alpha
.expr76 <- .expr60^(.expr72 - 1) * (.expr72 * .expr68)
.expr80 <- 1026576 * alpha^8
.expr84 <- 723680 * alpha^6
.expr85 <- 3/alpha
.expr89 <- .expr60^(.expr85 - 1) * (.expr85 * .expr68)
.expr97 <- 269325 * alpha^5
.expr103 <- 4/alpha
.expr107 <- .expr60^(.expr103 - 1) * (.expr103 * .expr68)
.expr112 <- 63273 * alpha^4
.expr113 <- 5/alpha
.expr117 <- .expr60^(.expr113 - 1) * (.expr113 * .expr68)
.expr129 <- 9450 * alpha^3
.expr139 <- 6/alpha
.expr143 <- .expr60^(.expr139 - 1) * (.expr139 * .expr68)
.expr148 <- 870 * alpha^2
.expr149 <- 7/alpha
.expr153 <- .expr60^(.expr149 - 1) * (.expr149 * .expr68)
.expr168 <- 45 * alpha
.expr182 <- 8/alpha
.expr186 <- .expr60^(.expr182 - 1) * (.expr182 * .expr68)
.expr206 <- 9/alpha
.expr228 <- .expr60^.expr61
.expr234 <- .expr60^.expr72
.expr242 <- .expr60^.expr85
.expr252 <- .expr60^.expr103
.expr264 <- .expr60^.expr113
.expr278 <- .expr60^.expr139
.expr294 <- .expr60^.expr149
.expr312 <- .expr60^.expr182
.expr333 <- .expr3 + 362880 * alpha^9 + .expr80 * (.expr3 +
.expr228) + .expr39 * (1 - 3 * .expr228 + .expr234) +
.expr84 * (.expr3 + 7 * .expr228 - 6 * .expr234 + .expr242) +
.expr97 * (1 - 15 * .expr228 + 25 * .expr234 - 10 * .expr242 +
.expr252) + .expr112 * (.expr3 + 31 * .expr228 -
90 * .expr234 + 65 * .expr242 - 15 * .expr252 + .expr264) +
.expr129 * (1 - 63 * .expr228 + 301 * .expr234 - 350 *
.expr242 + 140 * .expr252 - 21 * .expr264 + .expr278) +
.expr148 * (.expr3 + 127 * .expr228 - 966 * .expr234 +
1701 * .expr242 - 1050 * .expr252 + 266 * .expr264 -
28 * .expr278 + .expr294) + .expr168 * (1 - 255 *
.expr228 + 3025 * .expr234 - 7770 * .expr242 + 6951 *
.expr252 - 2646 * .expr264 + 462 * .expr278 - 36 * .expr294 +
.expr312) + 511 * .expr228 - 9330 * .expr234 + 34105 *
.expr242 - 42525 * .expr252 + 22827 * .expr264 - 5880 *
.expr278 + 750 * .expr294 - 45 * .expr312 + .expr60^.expr206
.expr337 <- -10 + .expr61
.expr338 <- .expr60^.expr337
.expr340 <- .expr37 * .expr333
.expr347 <- .expr58^.expr4
.expr349 <- E^.expr228
.expr359 <- .expr349 * u1 * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9
.value <- ((.expr37 * (.expr39 * (3 * .expr70 - .expr76) -
.expr80 * .expr70 - .expr84 * (.expr89 + (7 * .expr70 -
6 * .expr76)) + .expr97 * (15 * .expr70 - 25 * .expr76 +
10 * .expr89 - .expr107) - .expr112 * (.expr117 + (65 *
.expr89 + (31 * .expr70 - 90 * .expr76) - 15 * .expr107)) +
.expr129 * (63 * .expr70 - 301 * .expr76 + 350 * .expr89 -
140 * .expr107 + 21 * .expr117 - .expr143) - .expr148 *
(.expr153 + (266 * .expr117 + (1701 * .expr89 + (127 *
.expr70 - 966 * .expr76) - 1050 * .expr107) - 28 *
.expr143)) + .expr168 * (255 * .expr70 - 3025 * .expr76 +
7770 * .expr89 - 6951 * .expr107 + 2646 * .expr117 -
462 * .expr143 + 36 * .expr153 - .expr186) - 511 * .expr70 +
9330 * .expr76 - 34105 * .expr89 + 42525 * .expr107 -
22827 * .expr117 + 5880 * .expr143 - 750 * .expr153 +
45 * .expr186 - .expr60^(.expr206 - 1) * (.expr206 *
.expr68)) - .expr2^(.expr4 - 1) * (.expr4 * .expr66) *
.expr8 * .expr12 * .expr16 * .expr20 * .expr24 * .expr28 *
.expr32 * .expr36 * .expr333) * .expr338 - .expr340 *
(.expr60^(.expr337 - 1) * (.expr337 * .expr68))) * .expr347/.expr359 -
.expr340 * .expr338 * .expr347 * ((.expr349 - .expr349 *
(log(E) * .expr70) * u1) * u10 * u2 * u3 * u4 * u5 *
u6 * u7 * u8 * u9)/.expr359^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.pdfDerWrtPar.expr` <-
expression(-((((-log(u1))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))))) - ((-log(u1))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha)) * (1/alpha^2)))/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1)) - ((-log(u1))^alpha)^(1/alpha) * (E^((-log(u1))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))))) - ((-log(u1))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha)) * (1/alpha^2)))) * u1 * log(u1))/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1))^2), ((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) +
(-log(u1))^(-1 + alpha) * (1 + (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2))))) * ((-log(u1))^alpha +
(-log(u2))^alpha)^(-2 + 1/alpha) + (-log(u1))^(-1 + alpha) *
(-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha)^((-2 + 1/alpha) -
1) * ((-2 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(-2 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2)))) * (-log(u2))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-1 + alpha + ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha)^(-2 +
1/alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * u1 * u2) - ((-log(u1))^(-1 +
alpha) * (-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha)^(-2 + 1/alpha) * (-log(u2))^(-1 +
alpha)) * (E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2)))) * u1 * u2)/(E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * u1 * u2)^2, (((((-log(u1))^(-1 +
alpha) * log((-log(u1))) * (-log(u2))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (1 +
2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(2/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (2 * (2 * alpha) + (3 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) + 3 * alpha *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2)))) -
3 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (2/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^((-3 + 1/alpha) - 1) *
((-3 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * (log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)) * (1/alpha^2)))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * ((-log(u3))^(-1 + alpha) * log((-log(u3)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) * u1 * u2 *
u3) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * (-log(u3))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3)/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) *
u1 * u2 * u3)^2, ((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(6 * (3 * alpha^2) + (11 * (2 * alpha) * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
11 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2)))) + (6 * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 6 * alpha * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)) * (1/alpha^2))))) + 7 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) - 1) *
((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)) * (2/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(3/alpha^2))))) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(-4 + 1/alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((-4 + 1/alpha) - 1) * ((-4 + 1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * (log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)) * (1/alpha^2)))) *
(-log(u4))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 + 11 *
alpha^2 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * ((-log(u4))^(-1 + alpha) * log((-log(u4)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 + 11 *
alpha^2 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * (-log(u4))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2)))) * u1 * u2 * u3 * u4)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4)^2, -((((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-log(u4))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-1 - 24 *
alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) - 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(4/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (15 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2))) -
(24 * (4 * alpha^3) + (50 * (3 * alpha^2) * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) + 50 * alpha^3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2)))) +
(35 * (2 * alpha) * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) +
35 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (2/alpha^2)) - 3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2))))) +
(10 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
10 * alpha * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (1/alpha^2))) - 6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (2/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (3/alpha^2)))))) - 25 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) - 1) *
((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (2/alpha^2))) +
10 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (3/alpha^2))) -
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((4/alpha) - 1) *
((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (4/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 -
50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((-5 + 1/alpha) -
1) * ((-5 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(-5 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (1/alpha^2)))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-1 -
24 * alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) - 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(4/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(-5 +
1/alpha) * ((-log(u5))^(-1 + alpha) * log((-log(u5)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5) - ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 - 50 * alpha^3 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) - 35 *
alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) - 10 *
alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(3/alpha)) + 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(4/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(-5 +
1/alpha) * (-log(u5))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5)^2), ((((((((-log(u1))^(-1 + alpha) *
log((-log(u1))) * (-log(u2))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
((-log(u3))^(-1 + alpha) * log((-log(u3))))) * (-log(u4))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * ((-log(u4))^(-1 + alpha) * log((-log(u4))))) *
(-log(u5))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
((-log(u5))^(-1 + alpha) * log((-log(u5))))) * (-1 + 120 *
alpha^5 + 274 * alpha^4 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) + 85 * alpha^2 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(120 * (5 * alpha^4) + (274 * (4 * alpha^3) * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
274 * alpha^4 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (1/alpha^2)))) + (225 *
(3 * alpha^2) * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
225 * alpha^3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (2/alpha^2)) - 3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))))) +
(85 * (2 * alpha) * (-1 + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
85 * alpha^2 * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (1/alpha^2))) - 6 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (2/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (3/alpha^2))))) +
(15 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
15 * alpha * (25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (2/alpha^2))) - 15 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))) -
10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) *
(3/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (4/alpha^2))))) +
31 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))) -
90 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (2/alpha^2))) +
65 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (3/alpha^2))) -
15 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (4/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (5/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 + 274 * alpha^4 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha)) + 85 * alpha^2 * (-1 + 7 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((-6 +
1/alpha) - 1) * ((-6 + 1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(-6 + 1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)) *
(1/alpha^2)))) * (-log(u6))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-1 +
120 * alpha^5 + 274 * alpha^4 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) + 15 *
alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha)) + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(5/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(-6 + 1/alpha) * ((-log(u6))^(-1 + alpha) *
log((-log(u6)))))/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6) -
((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-1 + 120 * alpha^5 + 274 * alpha^4 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) * (-log(u6))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5 * u6)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 *
u6)^2, -((((((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-log(u4))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * ((-log(u5))^(-1 +
alpha) * log((-log(u5))))) * (-log(u6))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * ((-log(u6))^(-1 +
alpha) * log((-log(u6))))) * (-1 - 720 * alpha^6 - 1764 *
alpha^5 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) - 1624 * alpha^4 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) - 175 * alpha^2 * (1 -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha)) - 21 * alpha *
(-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(63 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))) - (720 * (6 * alpha^5) + (1764 * (5 * alpha^4) *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) + 1764 * alpha^5 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2)))) + (1624 * (4 * alpha^3) * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) +
1624 * alpha^4 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))))) + (735 * (3 * alpha^2) * (-1 +
7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) + 735 * alpha^3 * (7 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (1/alpha^2))) - 6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (3/alpha^2))))) + (175 * (2 *
alpha) * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) + 175 * alpha^2 * (25 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (2/alpha^2))) - 15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))) - 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (3/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(4/alpha^2))))) + (21 * (-1 + 31 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
21 * alpha * (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2))) + 65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(3/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(4/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(5/alpha^2)))))) - 301 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2))) + 350 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (3/alpha^2))) - 140 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(4/alpha^2))) + 21 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) - 1) *
((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (5/alpha^2))) - (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(6/alpha^2))))) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(-7 + 1/alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-1 - 720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((-7 + 1/alpha) - 1) *
((-7 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(-7 +
1/alpha) * (log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (1/alpha^2)))) * (-log(u7))^(-1 + alpha) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-1 - 720 * alpha^6 - 1764 *
alpha^5 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) - 1624 *
alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(-7 +
1/alpha) * ((-log(u7))^(-1 + alpha) * log((-log(u7)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-1 - 720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) - 175 * alpha^2 *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha)) -
21 * alpha * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(6/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(-7 + 1/alpha) * (-log(u7))^(-1 + alpha)) *
(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2)))) * u1 * u2 * u3 * u4 * u5 * u6 * u7)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7)^2), ((((((((((-log(u1))^(-1 +
alpha) * log((-log(u1))) * (-log(u2))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
((-log(u3))^(-1 + alpha) * log((-log(u3))))) * (-log(u4))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * ((-log(u4))^(-1 + alpha) * log((-log(u4))))) *
(-log(u5))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
((-log(u5))^(-1 + alpha) * log((-log(u5))))) * (-log(u6))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * ((-log(u6))^(-1 + alpha) * log((-log(u6))))) * (-log(u7))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * ((-log(u7))^(-1 + alpha) *
log((-log(u7))))) * (-1 + 5040 * alpha^7 + 13068 * alpha^6 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) + 13132 *
alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) + 6769 *
alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha)) + 1960 * alpha^3 * (1 - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha)) + 322 * alpha^2 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 90 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + 65 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha)) + 28 * alpha * (1 - 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + 140 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) - 21 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(6/alpha)) + 127 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 1050 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + 266 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) - 28 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(7/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-log(u7))^(-1 + alpha) * (5040 * (7 * alpha^6) + (13068 *
(6 * alpha^5) * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) +
13068 * alpha^6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2)))) + (13132 * (5 * alpha^4) *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(2/alpha)) + 13132 * alpha^5 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2)) - 3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))))) + (6769 * (4 * alpha^3) *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
6769 * alpha^4 * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (2/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))))) + (1960 * (3 *
alpha^2) * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha)) + 1960 * alpha^3 * (25 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2))) - 15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 10 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (4/alpha^2))))) + (322 * (2 * alpha) *
(-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 90 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
322 * alpha^2 * (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 90 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (2/alpha^2))) +
65 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) - 15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (4/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (5/alpha^2))))) + (28 * (1 -
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + 301 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + 140 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) - 21 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(6/alpha)) + 28 * alpha * (301 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2))) - 63 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 350 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) + 140 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (4/alpha^2))) - 21 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (5/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((6/alpha) - 1) * ((6/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (6/alpha^2))))) + 127 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 966 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2))) + 1701 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) - 1050 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (4/alpha^2))) + 266 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (5/alpha^2))) - 28 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((6/alpha) - 1) * ((6/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (6/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((7/alpha) - 1) * ((7/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (7/alpha^2))))) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(-8 + 1/alpha) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-log(u7))^(-1 + alpha) * (-1 + 5040 * alpha^7 + 13068 *
alpha^6 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) + 13132 *
alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) + 6769 *
alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha)) + 1960 * alpha^3 * (1 - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha)) + 322 * alpha^2 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 90 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + 65 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha)) + 28 * alpha * (1 - 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + 140 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) - 21 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(6/alpha)) + 127 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 1050 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + 266 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) - 28 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(7/alpha)) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((-8 +
1/alpha) - 1) * ((-8 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(-8 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2)))) * (-log(u8))^(-1 + alpha) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-1 +
5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
((-log(u8))^(-1 + alpha) * log((-log(u8)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6 *
u7 * u8) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
(-log(u8))^(-1 + alpha)) * (E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6 *
u7 * u8)^2, (((((((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-log(u4))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * ((-log(u5))^(-1 +
alpha) * log((-log(u5))))) * (-log(u6))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * ((-log(u6))^(-1 +
alpha) * log((-log(u6))))) * (-log(u7))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * ((-log(u7))^(-1 + alpha) * log((-log(u7))))) * (-log(u8))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
((-log(u8))^(-1 + alpha) * log((-log(u8))))) * (1 + 40320 *
alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 118124 * alpha^6 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) + 22449 *
alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 4536 * alpha^3 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 1701 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 +
alpha) * (40320 * (8 * alpha^7) + (109584 * (7 * alpha^6) *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
109584 * alpha^7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) + (118124 * (6 * alpha^5) *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
118124 * alpha^6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))))) + (67284 * (5 * alpha^4) *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
67284 * alpha^5 * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))))) + (22449 * (4 * alpha^3) *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
22449 * alpha^4 * (25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(4/alpha^2))))) + (4536 * (3 * alpha^2) * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
4536 * alpha^3 * (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) + 65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(4/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))))) + (546 * (2 * alpha) * (1 -
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
546 * alpha^2 * (301 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 63 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 350 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (3/alpha^2))) +
140 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (4/alpha^2))) -
21 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (5/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (6/alpha^2))))) +
(36 * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) +
36 * alpha * (127 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 966 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (2/alpha^2))) +
1701 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (3/alpha^2))) - 1050 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (4/alpha^2))) +
266 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (5/alpha^2))) - 28 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (6/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (7/alpha^2))))) -
255 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (1/alpha^2))) +
3025 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (2/alpha^2))) -
7770 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (3/alpha^2))) +
6951 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (4/alpha^2))) -
2646 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (5/alpha^2))) +
462 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (6/alpha^2))) -
36 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (7/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) -
1) * ((8/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (8/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (1 + 40320 * alpha^8 +
109584 * alpha^7 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 118124 * alpha^6 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) + 22449 *
alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 4536 * alpha^3 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 1701 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((-9 +
1/alpha) - 1) * ((-9 + 1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(-9 + 1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) * (-log(u9))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 118124 *
alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 67284 * alpha^5 * (-1 +
7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * ((-log(u9))^(-1 + alpha) * log((-log(u9)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) * (1 +
40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 118124 *
alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 67284 * alpha^5 * (-1 + 7 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 65 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 1701 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * (-log(u9))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9)^2, ((((((((((((-log(u1))^(-1 +
alpha) * log((-log(u1))) * (-log(u10))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u10))^(-1 + alpha) * log((-log(u10))))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) * log((-log(u3))))) *
(-log(u4))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * ((-log(u5))^(-1 + alpha) * log((-log(u5))))) * (-log(u6))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * ((-log(u6))^(-1 + alpha) *
log((-log(u6))))) * (-log(u7))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * ((-log(u7))^(-1 + alpha) *
log((-log(u7))))) * (-log(u8))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
((-log(u8))^(-1 + alpha) * log((-log(u8))))) * (-1 + 362880 *
alpha^9 + 1026576 * alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 1172700 *
alpha^7 * (1 - 3 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
723680 * alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
269325 * alpha^5 * (1 - 15 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 63273 * alpha^4 *
(-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (362880 * (9 * alpha^8) + (1026576 *
(8 * alpha^7) * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 1026576 *
alpha^8 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) + (1172700 * (7 * alpha^6) * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 1172700 *
alpha^7 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))))) + (723680 * (6 *
alpha^5) * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 723680 * alpha^6 * (7 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 6 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))))) + (269325 * (5 * alpha^4) * (1 - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 269325 * alpha^5 * (25 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 10 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))))) + (63273 * (4 *
alpha^3) * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 63273 * alpha^4 * (31 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 90 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + 65 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))))) + (9450 * (3 * alpha^2) * (1 - 63 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 350 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) - 21 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 9450 * alpha^3 * (301 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 63 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 350 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + 140 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) - 21 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) + (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))))) + (870 * (2 * alpha) *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 870 * alpha^2 * (127 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 966 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + 1701 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 1050 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) + 266 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) - 28 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(7/alpha^2))))) + (45 * (1 - 255 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 45 * alpha *
(3025 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 255 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 7770 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + 6951 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) *
((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) - 2646 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) + 462 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) *
((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))) - 36 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(7/alpha^2))) + (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) - 1) *
((8/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (8/alpha^2))))) + 511 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 9330 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + 34105 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 42525 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) + 22827 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) - 5880 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))) + 750 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(7/alpha^2))) - 45 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) - 1) * ((8/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (8/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((9/alpha) -
1) * ((9/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(9/alpha^2))))) * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(-10 + 1/alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 + 1026576 *
alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((-10 +
1/alpha) - 1) * ((-10 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(-10 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) * (-log(u9))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 + 1026576 *
alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * ((-log(u9))^(-1 + alpha) * log((-log(u9)))))/(E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
u1 * u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 + 1026576 *
alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * (-log(u9))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) * u1 * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9)/(E^((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u10 *
u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)^2)
`gumbelCopula.pdfDerWrtPar.algr` <-
expression({
.expr1 <- log(u1)
.expr2 <- -.expr1
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.expr11 <- .expr3^.expr4
.expr17 <- .expr3^(.expr4 - 1) * (.expr4 * (.expr3 * log(.expr2))) -
.expr11 * (log(.expr3) * (1/alpha^2))
.expr18 <- E^.expr11
.expr20 <- .expr18 * u1 * .expr1
.value <- -(.expr17/.expr20 - .expr11 * (.expr18 * (log(E) *
.expr17) * u1 * .expr1)/.expr20^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr4 <- -1 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr8 <- .expr2^alpha
.expr10 <- -log(u2)
.expr11 <- .expr10^alpha
.expr12 <- .expr8 + .expr11
.expr13 <- 1/alpha
.expr14 <- .expr12^.expr13
.expr15 <- .expr4 + .expr14
.expr20 <- log(.expr10)
.expr22 <- .expr8 * .expr6 + .expr11 * .expr20
.expr28 <- log(.expr12) * (1/alpha^2)
.expr30 <- .expr12^(.expr13 - 1) * (.expr13 * .expr22) -
.expr14 * .expr28
.expr35 <- -2 + .expr13
.expr36 <- .expr12^.expr35
.expr38 <- .expr5 * .expr15
.expr47 <- .expr10^.expr4
.expr49 <- .expr38 * .expr36
.expr53 <- E^.expr14
.expr55 <- .expr53 * u1 * u2
.value <- (((.expr5 * .expr6 * .expr15 + .expr5 * (1 + .expr30)) *
.expr36 + .expr38 * (.expr12^(.expr35 - 1) * (.expr35 *
.expr22) - .expr36 * .expr28)) * .expr47 + .expr49 *
(.expr47 * .expr20))/.expr55 - .expr49 * .expr47 * (.expr53 *
(log(E) * .expr30) * u1 * u2)/.expr55^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr16 <- alpha^2
.expr19 <- 3 * alpha
.expr20 <- .expr2^alpha
.expr21 <- .expr9^alpha
.expr24 <- -log(u3)
.expr25 <- .expr24^alpha
.expr26 <- .expr20 + .expr21 + .expr25
.expr27 <- 1/alpha
.expr28 <- .expr26^.expr27
.expr29 <- .expr3 + .expr28
.expr34 <- 2/alpha
.expr35 <- .expr26^.expr34
.expr36 <- 1 + 2 * .expr16 + .expr19 * .expr29 - 3 * .expr28 +
.expr35
.expr38 <- .expr5 * .expr10
.expr47 <- log(.expr24)
.expr49 <- .expr20 * .expr6 + .expr21 * .expr12 + .expr25 *
.expr47
.expr52 <- log(.expr26)
.expr54 <- .expr52 * (1/.expr16)
.expr56 <- .expr26^(.expr27 - 1) * (.expr27 * .expr49) -
.expr28 * .expr54
.expr74 <- -3 + .expr27
.expr75 <- .expr26^.expr74
.expr77 <- .expr38 * .expr36
.expr86 <- .expr24^.expr4
.expr88 <- .expr77 * .expr75
.expr92 <- E^.expr28
.expr95 <- .expr92 * u1 * u2 * u3
.value <- ((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr36 + .expr38 * (2 * (2 * alpha) + (3 *
.expr29 + .expr19 * .expr56) - 3 * .expr56 + (.expr26^(.expr34 -
1) * (.expr34 * .expr49) - .expr35 * (.expr52 * (2/.expr16))))) *
.expr75 + .expr77 * (.expr26^(.expr74 - 1) * (.expr74 *
.expr49) - .expr75 * .expr54)) * .expr86 + .expr88 *
(.expr86 * .expr47))/.expr95 - .expr88 * .expr86 * (.expr92 *
(log(E) * .expr56) * u1 * u2 * u3)/.expr95^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr28 <- alpha^2
.expr29 <- 11 * .expr28
.expr30 <- .expr2^alpha
.expr31 <- .expr9^alpha
.expr33 <- .expr17^alpha
.expr36 <- -log(u4)
.expr37 <- .expr36^alpha
.expr38 <- .expr30 + .expr31 + .expr33 + .expr37
.expr39 <- 1/alpha
.expr40 <- .expr38^.expr39
.expr41 <- .expr3 + .expr40
.expr44 <- 6 * alpha
.expr47 <- 2/alpha
.expr48 <- .expr38^.expr47
.expr49 <- 1 - 3 * .expr40 + .expr48
.expr56 <- 3/alpha
.expr57 <- .expr38^.expr56
.expr58 <- .expr3 + 6 * alpha^3 + .expr29 * .expr41 + .expr44 *
.expr49 + 7 * .expr40 - 6 * .expr48 + .expr57
.expr60 <- .expr20 * .expr18
.expr73 <- log(.expr36)
.expr75 <- .expr30 * .expr6 + .expr31 * .expr12 + .expr33 *
.expr21 + .expr37 * .expr73
.expr78 <- log(.expr38)
.expr80 <- .expr78 * (1/.expr28)
.expr82 <- .expr38^(.expr39 - 1) * (.expr39 * .expr75) -
.expr40 * .expr80
.expr94 <- .expr38^(.expr47 - 1) * (.expr47 * .expr75) -
.expr48 * (.expr78 * (2/.expr28))
.expr116 <- -4 + .expr39
.expr117 <- .expr38^.expr116
.expr119 <- .expr60 * .expr58
.expr128 <- .expr36^.expr4
.expr130 <- .expr119 * .expr117
.expr134 <- E^.expr40
.expr138 <- .expr134 * u1 * u2 * u3 * u4
.value <- (((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr58 + .expr60 * (6 * (3 * .expr28) + (11 * (2 * alpha) *
.expr41 + .expr29 * .expr82) + (6 * .expr49 + .expr44 *
(.expr94 - 3 * .expr82)) + 7 * .expr82 - 6 * .expr94 +
(.expr38^(.expr56 - 1) * (.expr56 * .expr75) - .expr57 *
(.expr78 * (3/.expr28))))) * .expr117 + .expr119 *
(.expr38^(.expr116 - 1) * (.expr116 * .expr75) - .expr117 *
.expr80)) * .expr128 + .expr130 * (.expr128 * .expr73))/.expr138 -
.expr130 * .expr128 * (.expr134 * (log(E) * .expr82) *
u1 * u2 * u3 * u4)/.expr138^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr37 <- alpha^3
.expr38 <- 50 * .expr37
.expr39 <- .expr2^alpha
.expr40 <- .expr9^alpha
.expr42 <- .expr17^alpha
.expr44 <- .expr26^alpha
.expr47 <- -log(u5)
.expr48 <- .expr47^alpha
.expr49 <- .expr39 + .expr40 + .expr42 + .expr44 + .expr48
.expr50 <- 1/alpha
.expr51 <- .expr49^.expr50
.expr52 <- .expr3 + .expr51
.expr55 <- alpha^2
.expr56 <- 35 * .expr55
.expr59 <- 2/alpha
.expr60 <- .expr49^.expr59
.expr61 <- 1 - 3 * .expr51 + .expr60
.expr64 <- 10 * alpha
.expr69 <- 3/alpha
.expr70 <- .expr49^.expr69
.expr71 <- .expr3 + 7 * .expr51 - 6 * .expr60 + .expr70
.expr80 <- 4/alpha
.expr81 <- .expr49^.expr80
.expr82 <- .expr3 - 24 * alpha^4 - .expr38 * .expr52 - .expr56 *
.expr61 - .expr64 * .expr71 + 15 * .expr51 - 25 * .expr60 +
10 * .expr70 - .expr81
.expr84 <- .expr29 * .expr27
.expr94 <- log(.expr47)
.expr96 <- .expr39 * .expr6 + .expr40 * .expr12 + .expr42 *
.expr21 + .expr44 * .expr30 + .expr48 * .expr94
.expr99 <- log(.expr49)
.expr101 <- .expr99 * (1/.expr55)
.expr103 <- .expr49^(.expr50 - 1) * (.expr50 * .expr96) -
.expr51 * .expr101
.expr123 <- .expr49^(.expr59 - 1) * (.expr59 * .expr96) -
.expr60 * (.expr99 * (2/.expr55))
.expr140 <- .expr49^(.expr69 - 1) * (.expr69 * .expr96) -
.expr70 * (.expr99 * (3/.expr55))
.expr162 <- -5 + .expr50
.expr163 <- .expr49^.expr162
.expr165 <- .expr84 * .expr82
.expr174 <- .expr47^.expr4
.expr176 <- .expr165 * .expr163
.expr180 <- E^.expr51
.expr185 <- .expr180 * u1 * u2 * u3 * u4 * u5
.value <- -(((((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr27 + .expr29 * (.expr27 * .expr30)) * .expr82 +
.expr84 * (15 * .expr103 - (24 * (4 * .expr37) + (50 *
(3 * .expr55) * .expr52 + .expr38 * .expr103) + (35 *
(2 * alpha) * .expr61 + .expr56 * (.expr123 - 3 *
.expr103)) + (10 * .expr71 + .expr64 * (7 * .expr103 -
6 * .expr123 + .expr140))) - 25 * .expr123 + 10 *
.expr140 - (.expr49^(.expr80 - 1) * (.expr80 * .expr96) -
.expr81 * (.expr99 * (4/.expr55))))) * .expr163 +
.expr165 * (.expr49^(.expr162 - 1) * (.expr162 * .expr96) -
.expr163 * .expr101)) * .expr174 + .expr176 * (.expr174 *
.expr94))/.expr185 - .expr176 * .expr174 * (.expr180 *
(log(E) * .expr103) * u1 * u2 * u3 * u4 * u5)/.expr185^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr46 <- alpha^4
.expr47 <- 274 * .expr46
.expr48 <- .expr2^alpha
.expr49 <- .expr9^alpha
.expr51 <- .expr17^alpha
.expr53 <- .expr26^alpha
.expr55 <- .expr35^alpha
.expr58 <- -log(u6)
.expr59 <- .expr58^alpha
.expr60 <- .expr48 + .expr49 + .expr51 + .expr53 + .expr55 +
.expr59
.expr61 <- 1/alpha
.expr62 <- .expr60^.expr61
.expr63 <- .expr3 + .expr62
.expr66 <- alpha^3
.expr67 <- 225 * .expr66
.expr70 <- 2/alpha
.expr71 <- .expr60^.expr70
.expr72 <- 1 - 3 * .expr62 + .expr71
.expr75 <- alpha^2
.expr76 <- 85 * .expr75
.expr81 <- 3/alpha
.expr82 <- .expr60^.expr81
.expr83 <- .expr3 + 7 * .expr62 - 6 * .expr71 + .expr82
.expr86 <- 15 * alpha
.expr93 <- 4/alpha
.expr94 <- .expr60^.expr93
.expr95 <- 1 - 15 * .expr62 + 25 * .expr71 - 10 * .expr82 +
.expr94
.expr106 <- 5/alpha
.expr107 <- .expr60^.expr106
.expr108 <- .expr3 + 120 * alpha^5 + .expr47 * .expr63 +
.expr67 * .expr72 + .expr76 * .expr83 + .expr86 * .expr95 +
31 * .expr62 - 90 * .expr71 + 65 * .expr82 - 15 * .expr94 +
.expr107
.expr110 <- .expr38 * .expr36
.expr127 <- log(.expr58)
.expr129 <- .expr48 * .expr6 + .expr49 * .expr12 + .expr51 *
.expr21 + .expr53 * .expr30 + .expr55 * .expr39 + .expr59 *
.expr127
.expr132 <- log(.expr60)
.expr134 <- .expr132 * (1/.expr75)
.expr136 <- .expr60^(.expr61 - 1) * (.expr61 * .expr129) -
.expr62 * .expr134
.expr150 <- .expr60^(.expr70 - 1) * (.expr70 * .expr129) -
.expr71 * (.expr132 * (2/.expr75))
.expr169 <- .expr60^(.expr81 - 1) * (.expr81 * .expr129) -
.expr82 * (.expr132 * (3/.expr75))
.expr187 <- .expr60^(.expr93 - 1) * (.expr93 * .expr129) -
.expr94 * (.expr132 * (4/.expr75))
.expr212 <- -6 + .expr61
.expr213 <- .expr60^.expr212
.expr215 <- .expr110 * .expr108
.expr224 <- .expr58^.expr4
.expr226 <- .expr215 * .expr213
.expr230 <- E^.expr62
.expr236 <- .expr230 * u1 * u2 * u3 * u4 * u5 * u6
.value <- (((((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr27 + .expr29 * (.expr27 * .expr30)) * .expr36 +
.expr38 * (.expr36 * .expr39)) * .expr108 + .expr110 *
(120 * (5 * .expr46) + (274 * (4 * .expr66) * .expr63 +
.expr47 * .expr136) + (225 * (3 * .expr75) * .expr72 +
.expr67 * (.expr150 - 3 * .expr136)) + (85 * (2 *
alpha) * .expr83 + .expr76 * (7 * .expr136 - 6 *
.expr150 + .expr169)) + (15 * .expr95 + .expr86 *
(25 * .expr150 - 15 * .expr136 - 10 * .expr169 +
.expr187)) + 31 * .expr136 - 90 * .expr150 +
65 * .expr169 - 15 * .expr187 + (.expr60^(.expr106 -
1) * (.expr106 * .expr129) - .expr107 * (.expr132 *
(5/.expr75))))) * .expr213 + .expr215 * (.expr60^(.expr212 -
1) * (.expr212 * .expr129) - .expr213 * .expr134)) *
.expr224 + .expr226 * (.expr224 * .expr127))/.expr236 -
.expr226 * .expr224 * (.expr230 * (log(E) * .expr136) *
u1 * u2 * u3 * u4 * u5 * u6)/.expr236^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u6)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr55 <- alpha^5
.expr56 <- 1764 * .expr55
.expr57 <- .expr2^alpha
.expr58 <- .expr9^alpha
.expr60 <- .expr17^alpha
.expr62 <- .expr26^alpha
.expr64 <- .expr35^alpha
.expr66 <- .expr44^alpha
.expr69 <- -log(u7)
.expr70 <- .expr69^alpha
.expr71 <- .expr57 + .expr58 + .expr60 + .expr62 + .expr64 +
.expr66 + .expr70
.expr72 <- 1/alpha
.expr73 <- .expr71^.expr72
.expr74 <- .expr3 + .expr73
.expr77 <- alpha^4
.expr78 <- 1624 * .expr77
.expr81 <- 2/alpha
.expr82 <- .expr71^.expr81
.expr83 <- 1 - 3 * .expr73 + .expr82
.expr86 <- alpha^3
.expr87 <- 735 * .expr86
.expr92 <- 3/alpha
.expr93 <- .expr71^.expr92
.expr94 <- .expr3 + 7 * .expr73 - 6 * .expr82 + .expr93
.expr97 <- alpha^2
.expr98 <- 175 * .expr97
.expr105 <- 4/alpha
.expr106 <- .expr71^.expr105
.expr107 <- 1 - 15 * .expr73 + 25 * .expr82 - 10 * .expr93 +
.expr106
.expr110 <- 21 * alpha
.expr119 <- 5/alpha
.expr120 <- .expr71^.expr119
.expr121 <- .expr3 + 31 * .expr73 - 90 * .expr82 + 65 * .expr93 -
15 * .expr106 + .expr120
.expr134 <- 6/alpha
.expr135 <- .expr71^.expr134
.expr136 <- .expr3 - 720 * alpha^6 - .expr56 * .expr74 -
.expr78 * .expr83 - .expr87 * .expr94 - .expr98 * .expr107 -
.expr110 * .expr121 + 63 * .expr73 - 301 * .expr82 +
350 * .expr93 - 140 * .expr106 + 21 * .expr120 - .expr135
.expr138 <- .expr47 * .expr45
.expr152 <- log(.expr69)
.expr154 <- .expr57 * .expr6 + .expr58 * .expr12 + .expr60 *
.expr21 + .expr62 * .expr30 + .expr64 * .expr39 + .expr66 *
.expr48 + .expr70 * .expr152
.expr157 <- log(.expr71)
.expr159 <- .expr157 * (1/.expr97)
.expr161 <- .expr71^(.expr72 - 1) * (.expr72 * .expr154) -
.expr73 * .expr159
.expr181 <- .expr71^(.expr81 - 1) * (.expr81 * .expr154) -
.expr82 * (.expr157 * (2/.expr97))
.expr200 <- .expr71^(.expr92 - 1) * (.expr92 * .expr154) -
.expr93 * (.expr157 * (3/.expr97))
.expr220 <- .expr71^(.expr105 - 1) * (.expr105 * .expr154) -
.expr106 * (.expr157 * (4/.expr97))
.expr240 <- .expr71^(.expr119 - 1) * (.expr119 * .expr154) -
.expr120 * (.expr157 * (5/.expr97))
.expr266 <- -7 + .expr72
.expr267 <- .expr71^.expr266
.expr269 <- .expr138 * .expr136
.expr278 <- .expr69^.expr4
.expr280 <- .expr269 * .expr267
.expr284 <- E^.expr73
.expr291 <- .expr284 * u1 * u2 * u3 * u4 * u5 * u6 * u7
.value <- -(((((((((.expr5 * .expr6 * .expr10 + .expr5 *
(.expr10 * .expr12)) * .expr18 + .expr20 * (.expr18 *
.expr21)) * .expr27 + .expr29 * (.expr27 * .expr30)) *
.expr36 + .expr38 * (.expr36 * .expr39)) * .expr45 +
.expr47 * (.expr45 * .expr48)) * .expr136 + .expr138 *
(63 * .expr161 - (720 * (6 * .expr55) + (1764 * (5 *
.expr77) * .expr74 + .expr56 * .expr161) + (1624 *
(4 * .expr86) * .expr83 + .expr78 * (.expr181 - 3 *
.expr161)) + (735 * (3 * .expr97) * .expr94 + .expr87 *
(7 * .expr161 - 6 * .expr181 + .expr200)) + (175 *
(2 * alpha) * .expr107 + .expr98 * (25 * .expr181 -
15 * .expr161 - 10 * .expr200 + .expr220)) + (21 *
.expr121 + .expr110 * (31 * .expr161 - 90 * .expr181 +
65 * .expr200 - 15 * .expr220 + .expr240))) - 301 *
.expr181 + 350 * .expr200 - 140 * .expr220 + 21 *
.expr240 - (.expr71^(.expr134 - 1) * (.expr134 *
.expr154) - .expr135 * (.expr157 * (6/.expr97))))) *
.expr267 + .expr269 * (.expr71^(.expr266 - 1) * (.expr266 *
.expr154) - .expr267 * .expr159)) * .expr278 + .expr280 *
(.expr278 * .expr152))/.expr291 - .expr280 * .expr278 *
(.expr284 * (log(E) * .expr161) * u1 * u2 * u3 * u4 *
u5 * u6 * u7)/.expr291^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u6)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr53 <- -log(u7)
.expr54 <- .expr53^.expr4
.expr56 <- .expr47 * .expr45
.expr57 <- log(.expr53)
.expr64 <- alpha^6
.expr65 <- 13068 * .expr64
.expr66 <- .expr2^alpha
.expr67 <- .expr9^alpha
.expr69 <- .expr17^alpha
.expr71 <- .expr26^alpha
.expr73 <- .expr35^alpha
.expr75 <- .expr44^alpha
.expr77 <- .expr53^alpha
.expr80 <- -log(u8)
.expr81 <- .expr80^alpha
.expr82 <- .expr66 + .expr67 + .expr69 + .expr71 + .expr73 +
.expr75 + .expr77 + .expr81
.expr83 <- 1/alpha
.expr84 <- .expr82^.expr83
.expr85 <- .expr3 + .expr84
.expr88 <- alpha^5
.expr89 <- 13132 * .expr88
.expr92 <- 2/alpha
.expr93 <- .expr82^.expr92
.expr94 <- 1 - 3 * .expr84 + .expr93
.expr97 <- alpha^4
.expr98 <- 6769 * .expr97
.expr103 <- 3/alpha
.expr104 <- .expr82^.expr103
.expr105 <- .expr3 + 7 * .expr84 - 6 * .expr93 + .expr104
.expr108 <- alpha^3
.expr109 <- 1960 * .expr108
.expr116 <- 4/alpha
.expr117 <- .expr82^.expr116
.expr118 <- 1 - 15 * .expr84 + 25 * .expr93 - 10 * .expr104 +
.expr117
.expr121 <- alpha^2
.expr122 <- 322 * .expr121
.expr131 <- 5/alpha
.expr132 <- .expr82^.expr131
.expr133 <- .expr3 + 31 * .expr84 - 90 * .expr93 + 65 * .expr104 -
15 * .expr117 + .expr132
.expr136 <- 28 * alpha
.expr147 <- 6/alpha
.expr148 <- .expr82^.expr147
.expr149 <- 1 - 63 * .expr84 + 301 * .expr93 - 350 * .expr104 +
140 * .expr117 - 21 * .expr132 + .expr148
.expr164 <- 7/alpha
.expr165 <- .expr82^.expr164
.expr166 <- .expr3 + 5040 * alpha^7 + .expr65 * .expr85 +
.expr89 * .expr94 + .expr98 * .expr105 + .expr109 * .expr118 +
.expr122 * .expr133 + .expr136 * .expr149 + 127 * .expr84 -
966 * .expr93 + 1701 * .expr104 - 1050 * .expr117 + 266 *
.expr132 - 28 * .expr148 + .expr165
.expr168 <- .expr56 * .expr54
.expr189 <- log(.expr80)
.expr191 <- .expr66 * .expr6 + .expr67 * .expr12 + .expr69 *
.expr21 + .expr71 * .expr30 + .expr73 * .expr39 + .expr75 *
.expr48 + .expr77 * .expr57 + .expr81 * .expr189
.expr194 <- log(.expr82)
.expr196 <- .expr194 * (1/.expr121)
.expr198 <- .expr82^(.expr83 - 1) * (.expr83 * .expr191) -
.expr84 * .expr196
.expr212 <- .expr82^(.expr92 - 1) * (.expr92 * .expr191) -
.expr93 * (.expr194 * (2/.expr121))
.expr231 <- .expr82^(.expr103 - 1) * (.expr103 * .expr191) -
.expr104 * (.expr194 * (3/.expr121))
.expr251 <- .expr82^(.expr116 - 1) * (.expr116 * .expr191) -
.expr117 * (.expr194 * (4/.expr121))
.expr273 <- .expr82^(.expr131 - 1) * (.expr131 * .expr191) -
.expr132 * (.expr194 * (5/.expr121))
.expr295 <- .expr82^(.expr147 - 1) * (.expr147 * .expr191) -
.expr148 * (.expr194 * (6/.expr121))
.expr324 <- -8 + .expr83
.expr325 <- .expr82^.expr324
.expr327 <- .expr168 * .expr166
.expr336 <- .expr80^.expr4
.expr338 <- .expr327 * .expr325
.expr342 <- E^.expr84
.expr350 <- .expr342 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8
.value <- (((((((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr27 + .expr29 * (.expr27 * .expr30)) * .expr36 +
.expr38 * (.expr36 * .expr39)) * .expr45 + .expr47 *
(.expr45 * .expr48)) * .expr54 + .expr56 * (.expr54 *
.expr57)) * .expr166 + .expr168 * (5040 * (7 * .expr64) +
(13068 * (6 * .expr88) * .expr85 + .expr65 * .expr198) +
(13132 * (5 * .expr97) * .expr94 + .expr89 * (.expr212 -
3 * .expr198)) + (6769 * (4 * .expr108) * .expr105 +
.expr98 * (7 * .expr198 - 6 * .expr212 + .expr231)) +
(1960 * (3 * .expr121) * .expr118 + .expr109 * (25 *
.expr212 - 15 * .expr198 - 10 * .expr231 + .expr251)) +
(322 * (2 * alpha) * .expr133 + .expr122 * (31 * .expr198 -
90 * .expr212 + 65 * .expr231 - 15 * .expr251 + .expr273)) +
(28 * .expr149 + .expr136 * (301 * .expr212 - 63 * .expr198 -
350 * .expr231 + 140 * .expr251 - 21 * .expr273 +
.expr295)) + 127 * .expr198 - 966 * .expr212 + 1701 *
.expr231 - 1050 * .expr251 + 266 * .expr273 - 28 * .expr295 +
(.expr82^(.expr164 - 1) * (.expr164 * .expr191) - .expr165 *
(.expr194 * (7/.expr121))))) * .expr325 + .expr327 *
(.expr82^(.expr324 - 1) * (.expr324 * .expr191) - .expr325 *
.expr196)) * .expr336 + .expr338 * (.expr336 * .expr189))/.expr350 -
.expr338 * .expr336 * (.expr342 * (log(E) * .expr198) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8)/.expr350^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u6)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr53 <- -log(u7)
.expr54 <- .expr53^.expr4
.expr56 <- .expr47 * .expr45
.expr57 <- log(.expr53)
.expr62 <- -log(u8)
.expr63 <- .expr62^.expr4
.expr65 <- .expr56 * .expr54
.expr66 <- log(.expr62)
.expr73 <- alpha^7
.expr74 <- 109584 * .expr73
.expr75 <- .expr2^alpha
.expr76 <- .expr9^alpha
.expr78 <- .expr17^alpha
.expr80 <- .expr26^alpha
.expr82 <- .expr35^alpha
.expr84 <- .expr44^alpha
.expr86 <- .expr53^alpha
.expr88 <- .expr62^alpha
.expr91 <- -log(u9)
.expr92 <- .expr91^alpha
.expr93 <- .expr75 + .expr76 + .expr78 + .expr80 + .expr82 +
.expr84 + .expr86 + .expr88 + .expr92
.expr94 <- 1/alpha
.expr95 <- .expr93^.expr94
.expr96 <- .expr3 + .expr95
.expr99 <- alpha^6
.expr100 <- 118124 * .expr99
.expr103 <- 2/alpha
.expr104 <- .expr93^.expr103
.expr105 <- 1 - 3 * .expr95 + .expr104
.expr108 <- alpha^5
.expr109 <- 67284 * .expr108
.expr114 <- 3/alpha
.expr115 <- .expr93^.expr114
.expr116 <- .expr3 + 7 * .expr95 - 6 * .expr104 + .expr115
.expr119 <- alpha^4
.expr120 <- 22449 * .expr119
.expr127 <- 4/alpha
.expr128 <- .expr93^.expr127
.expr129 <- 1 - 15 * .expr95 + 25 * .expr104 - 10 * .expr115 +
.expr128
.expr132 <- alpha^3
.expr133 <- 4536 * .expr132
.expr142 <- 5/alpha
.expr143 <- .expr93^.expr142
.expr144 <- .expr3 + 31 * .expr95 - 90 * .expr104 + 65 *
.expr115 - 15 * .expr128 + .expr143
.expr147 <- alpha^2
.expr148 <- 546 * .expr147
.expr159 <- 6/alpha
.expr160 <- .expr93^.expr159
.expr161 <- 1 - 63 * .expr95 + 301 * .expr104 - 350 * .expr115 +
140 * .expr128 - 21 * .expr143 + .expr160
.expr164 <- 36 * alpha
.expr177 <- 7/alpha
.expr178 <- .expr93^.expr177
.expr179 <- .expr3 + 127 * .expr95 - 966 * .expr104 + 1701 *
.expr115 - 1050 * .expr128 + 266 * .expr143 - 28 * .expr160 +
.expr178
.expr196 <- 8/alpha
.expr197 <- .expr93^.expr196
.expr198 <- 1 + 40320 * alpha^8 + .expr74 * .expr96 + .expr100 *
.expr105 + .expr109 * .expr116 + .expr120 * .expr129 +
.expr133 * .expr144 + .expr148 * .expr161 + .expr164 *
.expr179 - 255 * .expr95 + 3025 * .expr104 - 7770 * .expr115 +
6951 * .expr128 - 2646 * .expr143 + 462 * .expr160 -
36 * .expr178 + .expr197
.expr200 <- .expr65 * .expr63
.expr223 <- log(.expr91)
.expr225 <- .expr75 * .expr6 + .expr76 * .expr12 + .expr78 *
.expr21 + .expr80 * .expr30 + .expr82 * .expr39 + .expr84 *
.expr48 + .expr86 * .expr57 + .expr88 * .expr66 + .expr92 *
.expr223
.expr228 <- log(.expr93)
.expr230 <- .expr228 * (1/.expr147)
.expr232 <- .expr93^(.expr94 - 1) * (.expr94 * .expr225) -
.expr95 * .expr230
.expr246 <- .expr93^(.expr103 - 1) * (.expr103 * .expr225) -
.expr104 * (.expr228 * (2/.expr147))
.expr265 <- .expr93^(.expr114 - 1) * (.expr114 * .expr225) -
.expr115 * (.expr228 * (3/.expr147))
.expr285 <- .expr93^(.expr127 - 1) * (.expr127 * .expr225) -
.expr128 * (.expr228 * (4/.expr147))
.expr307 <- .expr93^(.expr142 - 1) * (.expr142 * .expr225) -
.expr143 * (.expr228 * (5/.expr147))
.expr331 <- .expr93^(.expr159 - 1) * (.expr159 * .expr225) -
.expr160 * (.expr228 * (6/.expr147))
.expr355 <- .expr93^(.expr177 - 1) * (.expr177 * .expr225) -
.expr178 * (.expr228 * (7/.expr147))
.expr386 <- -9 + .expr94
.expr387 <- .expr93^.expr386
.expr389 <- .expr200 * .expr198
.expr398 <- .expr91^.expr4
.expr400 <- .expr389 * .expr387
.expr404 <- E^.expr95
.expr413 <- .expr404 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8 * u9
.value <- ((((((((((.expr5 * .expr6 * .expr10 + .expr5 *
(.expr10 * .expr12)) * .expr18 + .expr20 * (.expr18 *
.expr21)) * .expr27 + .expr29 * (.expr27 * .expr30)) *
.expr36 + .expr38 * (.expr36 * .expr39)) * .expr45 +
.expr47 * (.expr45 * .expr48)) * .expr54 + .expr56 *
(.expr54 * .expr57)) * .expr63 + .expr65 * (.expr63 *
.expr66)) * .expr198 + .expr200 * (40320 * (8 * .expr73) +
(109584 * (7 * .expr99) * .expr96 + .expr74 * .expr232) +
(118124 * (6 * .expr108) * .expr105 + .expr100 * (.expr246 -
3 * .expr232)) + (67284 * (5 * .expr119) * .expr116 +
.expr109 * (7 * .expr232 - 6 * .expr246 + .expr265)) +
(22449 * (4 * .expr132) * .expr129 + .expr120 * (25 *
.expr246 - 15 * .expr232 - 10 * .expr265 + .expr285)) +
(4536 * (3 * .expr147) * .expr144 + .expr133 * (31 *
.expr232 - 90 * .expr246 + 65 * .expr265 - 15 * .expr285 +
.expr307)) + (546 * (2 * alpha) * .expr161 + .expr148 *
(301 * .expr246 - 63 * .expr232 - 350 * .expr265 + 140 *
.expr285 - 21 * .expr307 + .expr331)) + (36 * .expr179 +
.expr164 * (127 * .expr232 - 966 * .expr246 + 1701 *
.expr265 - 1050 * .expr285 + 266 * .expr307 - 28 *
.expr331 + .expr355)) - 255 * .expr232 + 3025 * .expr246 -
7770 * .expr265 + 6951 * .expr285 - 2646 * .expr307 +
462 * .expr331 - 36 * .expr355 + (.expr93^(.expr196 -
1) * (.expr196 * .expr225) - .expr197 * (.expr228 * (8/.expr147))))) *
.expr387 + .expr389 * (.expr93^(.expr386 - 1) * (.expr386 *
.expr225) - .expr387 * .expr230)) * .expr398 + .expr400 *
(.expr398 * .expr223))/.expr413 - .expr400 * .expr398 *
(.expr404 * (log(E) * .expr232) * u1 * u2 * u3 * u4 *
u5 * u6 * u7 * u8 * u9)/.expr413^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u10)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u2)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u3)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u4)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u5)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr53 <- -log(u6)
.expr54 <- .expr53^.expr4
.expr56 <- .expr47 * .expr45
.expr57 <- log(.expr53)
.expr62 <- -log(u7)
.expr63 <- .expr62^.expr4
.expr65 <- .expr56 * .expr54
.expr66 <- log(.expr62)
.expr71 <- -log(u8)
.expr72 <- .expr71^.expr4
.expr74 <- .expr65 * .expr63
.expr75 <- log(.expr71)
.expr82 <- alpha^8
.expr83 <- 1026576 * .expr82
.expr84 <- .expr2^alpha
.expr85 <- .expr9^alpha
.expr87 <- .expr17^alpha
.expr89 <- .expr26^alpha
.expr91 <- .expr35^alpha
.expr93 <- .expr44^alpha
.expr95 <- .expr53^alpha
.expr97 <- .expr62^alpha
.expr99 <- .expr71^alpha
.expr102 <- -log(u9)
.expr103 <- .expr102^alpha
.expr104 <- .expr84 + .expr85 + .expr87 + .expr89 + .expr91 +
.expr93 + .expr95 + .expr97 + .expr99 + .expr103
.expr105 <- 1/alpha
.expr106 <- .expr104^.expr105
.expr107 <- .expr3 + .expr106
.expr110 <- alpha^7
.expr111 <- 1172700 * .expr110
.expr114 <- 2/alpha
.expr115 <- .expr104^.expr114
.expr116 <- 1 - 3 * .expr106 + .expr115
.expr119 <- alpha^6
.expr120 <- 723680 * .expr119
.expr125 <- 3/alpha
.expr126 <- .expr104^.expr125
.expr127 <- .expr3 + 7 * .expr106 - 6 * .expr115 + .expr126
.expr130 <- alpha^5
.expr131 <- 269325 * .expr130
.expr138 <- 4/alpha
.expr139 <- .expr104^.expr138
.expr140 <- 1 - 15 * .expr106 + 25 * .expr115 - 10 * .expr126 +
.expr139
.expr143 <- alpha^4
.expr144 <- 63273 * .expr143
.expr153 <- 5/alpha
.expr154 <- .expr104^.expr153
.expr155 <- .expr3 + 31 * .expr106 - 90 * .expr115 + 65 *
.expr126 - 15 * .expr139 + .expr154
.expr158 <- alpha^3
.expr159 <- 9450 * .expr158
.expr170 <- 6/alpha
.expr171 <- .expr104^.expr170
.expr172 <- 1 - 63 * .expr106 + 301 * .expr115 - 350 * .expr126 +
140 * .expr139 - 21 * .expr154 + .expr171
.expr175 <- alpha^2
.expr176 <- 870 * .expr175
.expr189 <- 7/alpha
.expr190 <- .expr104^.expr189
.expr191 <- .expr3 + 127 * .expr106 - 966 * .expr115 + 1701 *
.expr126 - 1050 * .expr139 + 266 * .expr154 - 28 * .expr171 +
.expr190
.expr194 <- 45 * alpha
.expr209 <- 8/alpha
.expr210 <- .expr104^.expr209
.expr211 <- 1 - 255 * .expr106 + 3025 * .expr115 - 7770 *
.expr126 + 6951 * .expr139 - 2646 * .expr154 + 462 *
.expr171 - 36 * .expr190 + .expr210
.expr230 <- 9/alpha
.expr231 <- .expr104^.expr230
.expr232 <- .expr3 + 362880 * alpha^9 + .expr83 * .expr107 +
.expr111 * .expr116 + .expr120 * .expr127 + .expr131 *
.expr140 + .expr144 * .expr155 + .expr159 * .expr172 +
.expr176 * .expr191 + .expr194 * .expr211 + 511 * .expr106 -
9330 * .expr115 + 34105 * .expr126 - 42525 * .expr139 +
22827 * .expr154 - 5880 * .expr171 + 750 * .expr190 -
45 * .expr210 + .expr231
.expr234 <- .expr74 * .expr72
.expr259 <- log(.expr102)
.expr261 <- .expr84 * .expr6 + .expr85 * .expr12 + .expr87 *
.expr21 + .expr89 * .expr30 + .expr91 * .expr39 + .expr93 *
.expr48 + .expr95 * .expr57 + .expr97 * .expr66 + .expr99 *
.expr75 + .expr103 * .expr259
.expr264 <- log(.expr104)
.expr266 <- .expr264 * (1/.expr175)
.expr268 <- .expr104^(.expr105 - 1) * (.expr105 * .expr261) -
.expr106 * .expr266
.expr282 <- .expr104^(.expr114 - 1) * (.expr114 * .expr261) -
.expr115 * (.expr264 * (2/.expr175))
.expr301 <- .expr104^(.expr125 - 1) * (.expr125 * .expr261) -
.expr126 * (.expr264 * (3/.expr175))
.expr321 <- .expr104^(.expr138 - 1) * (.expr138 * .expr261) -
.expr139 * (.expr264 * (4/.expr175))
.expr343 <- .expr104^(.expr153 - 1) * (.expr153 * .expr261) -
.expr154 * (.expr264 * (5/.expr175))
.expr367 <- .expr104^(.expr170 - 1) * (.expr170 * .expr261) -
.expr171 * (.expr264 * (6/.expr175))
.expr393 <- .expr104^(.expr189 - 1) * (.expr189 * .expr261) -
.expr190 * (.expr264 * (7/.expr175))
.expr419 <- .expr104^(.expr209 - 1) * (.expr209 * .expr261) -
.expr210 * (.expr264 * (8/.expr175))
.expr452 <- -10 + .expr105
.expr453 <- .expr104^.expr452
.expr455 <- .expr234 * .expr232
.expr464 <- .expr102^.expr4
.expr466 <- .expr455 * .expr453
.expr470 <- E^.expr106
.expr480 <- .expr470 * u1 * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9
.value <- (((((((((((.expr5 * .expr6 * .expr10 + .expr5 *
(.expr10 * .expr12)) * .expr18 + .expr20 * (.expr18 *
.expr21)) * .expr27 + .expr29 * (.expr27 * .expr30)) *
.expr36 + .expr38 * (.expr36 * .expr39)) * .expr45 +
.expr47 * (.expr45 * .expr48)) * .expr54 + .expr56 *
(.expr54 * .expr57)) * .expr63 + .expr65 * (.expr63 *
.expr66)) * .expr72 + .expr74 * (.expr72 * .expr75)) *
.expr232 + .expr234 * (362880 * (9 * .expr82) + (1026576 *
(8 * .expr110) * .expr107 + .expr83 * .expr268) + (1172700 *
(7 * .expr119) * .expr116 + .expr111 * (.expr282 - 3 *
.expr268)) + (723680 * (6 * .expr130) * .expr127 + .expr120 *
(7 * .expr268 - 6 * .expr282 + .expr301)) + (269325 *
(5 * .expr143) * .expr140 + .expr131 * (25 * .expr282 -
15 * .expr268 - 10 * .expr301 + .expr321)) + (63273 *
(4 * .expr158) * .expr155 + .expr144 * (31 * .expr268 -
90 * .expr282 + 65 * .expr301 - 15 * .expr321 + .expr343)) +
(9450 * (3 * .expr175) * .expr172 + .expr159 * (301 *
.expr282 - 63 * .expr268 - 350 * .expr301 + 140 *
.expr321 - 21 * .expr343 + .expr367)) + (870 * (2 *
alpha) * .expr191 + .expr176 * (127 * .expr268 - 966 *
.expr282 + 1701 * .expr301 - 1050 * .expr321 + 266 *
.expr343 - 28 * .expr367 + .expr393)) + (45 * .expr211 +
.expr194 * (3025 * .expr282 - 255 * .expr268 - 7770 *
.expr301 + 6951 * .expr321 - 2646 * .expr343 + 462 *
.expr367 - 36 * .expr393 + .expr419)) + 511 * .expr268 -
9330 * .expr282 + 34105 * .expr301 - 42525 * .expr321 +
22827 * .expr343 - 5880 * .expr367 + 750 * .expr393 -
45 * .expr419 + (.expr104^(.expr230 - 1) * (.expr230 *
.expr261) - .expr231 * (.expr264 * (9/.expr175))))) *
.expr453 + .expr455 * (.expr104^(.expr452 - 1) * (.expr452 *
.expr261) - .expr453 * .expr266)) * .expr464 + .expr466 *
(.expr464 * .expr259))/.expr480 - .expr466 * .expr464 *
(.expr470 * (log(E) * .expr268) * u1 * u10 * u2 * u3 *
u4 * u5 * u6 * u7 * u8 * u9)/.expr480^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.genfunDer.expr` <-
expression((alpha * (-log(u))^alpha)/(u * log(u)), (alpha * (-1 +
alpha - log(u)) * (-log(u))^(-2 + alpha))/u^2)
`gumbelCopula.genfunDer.algr` <-
expression({
.expr1 <- log(u)
.value <- alpha * (-.expr1)^alpha/(u * .expr1)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr3 <- log(u)
.value <- alpha * (-1 + alpha - .expr3) * (-.expr3)^(-2 +
alpha)/u^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
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## This file is not to be edited. It is generated by ../inst/docs/mathnb/exprPrep.R
`gumbelCopula.cdf.expr` <-
expression(E^(-((-log(u1))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)), E^(-((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)))
`gumbelCopula.cdf.algr` <-
expression({
.value <- E^-((-log(u1))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.value <- E^-((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.cdfDerWrtArg.expr` <-
expression(E^(-((-log(u1))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))), E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))), E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))),
E^(-((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))))
`gumbelCopula.cdfDerWrtArg.algr` <-
expression({
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.value <- E^-.expr3^.expr4 * (log(E) * (.expr3^(.expr4 -
1) * (.expr4 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr7 <- .expr2^alpha + (-log(u2))^alpha
.expr8 <- 1/alpha
.value <- E^-.expr7^.expr8 * (log(E) * (.expr7^(.expr8 -
1) * (.expr8 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr11 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha
.expr12 <- 1/alpha
.value <- E^-.expr11^.expr12 * (log(E) * (.expr11^(.expr12 -
1) * (.expr12 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr15 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha
.expr16 <- 1/alpha
.value <- E^-.expr15^.expr16 * (log(E) * (.expr15^(.expr16 -
1) * (.expr16 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr19 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha
.expr20 <- 1/alpha
.value <- E^-.expr19^.expr20 * (log(E) * (.expr19^(.expr20 -
1) * (.expr20 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr23 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha
.expr24 <- 1/alpha
.value <- E^-.expr23^.expr24 * (log(E) * (.expr23^(.expr24 -
1) * (.expr24 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr27 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha
.expr28 <- 1/alpha
.value <- E^-.expr27^.expr28 * (log(E) * (.expr27^(.expr28 -
1) * (.expr28 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr31 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha
.expr32 <- 1/alpha
.value <- E^-.expr31^.expr32 * (log(E) * (.expr31^(.expr32 -
1) * (.expr32 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr35 <- .expr2^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha
.expr36 <- 1/alpha
.value <- E^-.expr35^.expr36 * (log(E) * (.expr35^(.expr36 -
1) * (.expr36 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr39 <- .expr2^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha
.expr40 <- 1/alpha
.value <- E^-.expr39^.expr40 * (log(E) * (.expr39^(.expr40 -
1) * (.expr40 * (.expr2^(alpha - 1) * (alpha * (1/u1))))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.cdfDerWrtPar.expr` <-
expression(-(E^(-((-log(u1))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))))) -
((-log(u1))^alpha)^(1/alpha) * (log(((-log(u1))^alpha)) *
(1/alpha^2))))), -(E^(-((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2))))), -(E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2))))),
-(E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2))))), -(E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (1/alpha^2))))), -(E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))))),
-(E^(-((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))))), -(E^(-((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))))), -(E^(-((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (1/alpha^2))))),
-(E^(-((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) * (log(E) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))))))
`gumbelCopula.cdfDerWrtPar.algr` <-
expression({
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.expr5 <- .expr3^.expr4
.value <- -(E^-.expr5 * (log(E) * (.expr3^(.expr4 - 1) *
(.expr4 * (.expr3 * log(.expr2))) - .expr5 * (log(.expr3) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr7 <- .expr3 + .expr6
.expr8 <- 1/alpha
.expr9 <- .expr7^.expr8
.value <- -(E^-.expr9 * (log(E) * (.expr7^(.expr8 - 1) *
(.expr8 * (.expr3 * log(.expr2) + .expr6 * log(.expr5))) -
.expr9 * (log(.expr7) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr11 <- .expr3 + .expr6 + .expr10
.expr12 <- 1/alpha
.expr13 <- .expr11^.expr12
.value <- -(E^-.expr13 * (log(E) * (.expr11^(.expr12 - 1) *
(.expr12 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9))) - .expr13 * (log(.expr11) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr15 <- .expr3 + .expr6 + .expr10 + .expr14
.expr16 <- 1/alpha
.expr17 <- .expr15^.expr16
.value <- -(E^-.expr17 * (log(E) * (.expr15^(.expr16 - 1) *
(.expr16 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13))) -
.expr17 * (log(.expr15) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr19 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18
.expr20 <- 1/alpha
.expr21 <- .expr19^.expr20
.value <- -(E^-.expr21 * (log(E) * (.expr19^(.expr20 - 1) *
(.expr20 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17))) - .expr21 * (log(.expr19) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr23 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22
.expr24 <- 1/alpha
.expr25 <- .expr23^.expr24
.value <- -(E^-.expr25 * (log(E) * (.expr23^(.expr24 - 1) *
(.expr24 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21))) -
.expr25 * (log(.expr23) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr25 <- -log(u7)
.expr26 <- .expr25^alpha
.expr27 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26
.expr28 <- 1/alpha
.expr29 <- .expr27^.expr28
.value <- -(E^-.expr29 * (log(E) * (.expr27^(.expr28 - 1) *
(.expr28 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25))) - .expr29 * (log(.expr27) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr25 <- -log(u7)
.expr26 <- .expr25^alpha
.expr29 <- -log(u8)
.expr30 <- .expr29^alpha
.expr31 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26 + .expr30
.expr32 <- 1/alpha
.expr33 <- .expr31^.expr32
.value <- -(E^-.expr33 * (log(E) * (.expr31^(.expr32 - 1) *
(.expr32 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25) + .expr30 * log(.expr29))) -
.expr33 * (log(.expr31) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u2)
.expr6 <- .expr5^alpha
.expr9 <- -log(u3)
.expr10 <- .expr9^alpha
.expr13 <- -log(u4)
.expr14 <- .expr13^alpha
.expr17 <- -log(u5)
.expr18 <- .expr17^alpha
.expr21 <- -log(u6)
.expr22 <- .expr21^alpha
.expr25 <- -log(u7)
.expr26 <- .expr25^alpha
.expr29 <- -log(u8)
.expr30 <- .expr29^alpha
.expr33 <- -log(u9)
.expr34 <- .expr33^alpha
.expr35 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26 + .expr30 + .expr34
.expr36 <- 1/alpha
.expr37 <- .expr35^.expr36
.value <- -(E^-.expr37 * (log(E) * (.expr35^(.expr36 - 1) *
(.expr36 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25) + .expr30 * log(.expr29) +
.expr34 * log(.expr33))) - .expr37 * (log(.expr35) *
(1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- .expr2^alpha
.expr5 <- -log(u10)
.expr6 <- .expr5^alpha
.expr9 <- -log(u2)
.expr10 <- .expr9^alpha
.expr13 <- -log(u3)
.expr14 <- .expr13^alpha
.expr17 <- -log(u4)
.expr18 <- .expr17^alpha
.expr21 <- -log(u5)
.expr22 <- .expr21^alpha
.expr25 <- -log(u6)
.expr26 <- .expr25^alpha
.expr29 <- -log(u7)
.expr30 <- .expr29^alpha
.expr33 <- -log(u8)
.expr34 <- .expr33^alpha
.expr37 <- -log(u9)
.expr38 <- .expr37^alpha
.expr39 <- .expr3 + .expr6 + .expr10 + .expr14 + .expr18 +
.expr22 + .expr26 + .expr30 + .expr34 + .expr38
.expr40 <- 1/alpha
.expr41 <- .expr39^.expr40
.value <- -(E^-.expr41 * (log(E) * (.expr39^(.expr40 - 1) *
(.expr40 * (.expr3 * log(.expr2) + .expr6 * log(.expr5) +
.expr10 * log(.expr9) + .expr14 * log(.expr13) +
.expr18 * log(.expr17) + .expr22 * log(.expr21) +
.expr26 * log(.expr25) + .expr30 * log(.expr29) +
.expr34 * log(.expr33) + .expr38 * log(.expr37))) -
.expr41 * (log(.expr39) * (1/alpha^2)))))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.pdf.expr` <-
expression(-(((-log(u1))^alpha)^(1/alpha)/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1))), ((-log(u1))^(-1 + alpha) * (-1 + alpha +
((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha)^(-2 + 1/alpha) * (-log(u2))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * u1 * u2), ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (1 + 2 * alpha^2 + 3 *
alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * (-log(u3))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) * u1 * u2 *
u3), ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 + 11 * alpha^2 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * (-log(u4))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4), -(((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-1 - 24 * alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) - 35 * alpha^2 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) *
(-log(u5))^(-1 + alpha))/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5)), ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 + 274 * alpha^4 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha)) + 85 * alpha^2 * (-1 + 7 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) * (-log(u6))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6), -(((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-1 -
720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(-7 + 1/alpha) * (-log(u7))^(-1 +
alpha))/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6 *
u7)), ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
(-log(u8))^(-1 + alpha))/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8), ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 118124 *
alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 67284 * alpha^5 * (-1 +
7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * (-log(u9))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9), ((-log(u1))^(-1 + alpha) *
(-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 +
alpha) * (-1 + 362880 * alpha^9 + 1026576 * alpha^8 * (-1 +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 -
3 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * (-log(u9))^(-1 + alpha))/(E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
u1 * u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9))
`gumbelCopula.pdf.algr` <-
expression({
.expr1 <- log(u1)
.expr5 <- ((-.expr1)^alpha)^(1/alpha)
.value <- -(.expr5/(E^.expr5 * u1 * .expr1))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr4 <- -1 + alpha
.expr8 <- -log(u2)
.expr10 <- .expr2^alpha + .expr8^alpha
.expr11 <- 1/alpha
.expr12 <- .expr10^.expr11
.value <- .expr2^.expr4 * (.expr4 + .expr12) * .expr10^(-2 +
.expr11) * .expr8^.expr4/(E^.expr12 * u1 * u2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr18 <- -log(u3)
.expr20 <- .expr2^alpha + .expr7^alpha + .expr18^alpha
.expr21 <- 1/alpha
.expr22 <- .expr20^.expr21
.value <- .expr2^.expr4 * .expr7^.expr4 * (1 + 2 * alpha^2 +
3 * alpha * (.expr3 + .expr22) - 3 * .expr22 + .expr20^(2/alpha)) *
.expr20^(-3 + .expr21) * .expr18^.expr4/(E^.expr22 *
u1 * u2 * u3)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr25 <- -log(u4)
.expr27 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr25^alpha
.expr28 <- 1/alpha
.expr29 <- .expr27^.expr28
.expr37 <- .expr27^(2/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
(.expr3 + 6 * alpha^3 + 11 * alpha^2 * (.expr3 + .expr29) +
6 * alpha * (1 - 3 * .expr29 + .expr37) + 7 * .expr29 -
6 * .expr37 + .expr27^(3/alpha)) * .expr27^(-4 +
.expr28) * .expr25^.expr4/(E^.expr29 * u1 * u2 * u3 *
u4)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr31 <- -log(u5)
.expr33 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr31^alpha
.expr34 <- 1/alpha
.expr35 <- .expr33^.expr34
.expr44 <- .expr33^(2/alpha)
.expr54 <- .expr33^(3/alpha)
.value <- -(.expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * (.expr3 - 24 * alpha^4 - 50 * alpha^3 *
(.expr3 + .expr35) - 35 * alpha^2 * (1 - 3 * .expr35 +
.expr44) - 10 * alpha * (.expr3 + 7 * .expr35 - 6 * .expr44 +
.expr54) + 15 * .expr35 - 25 * .expr44 + 10 * .expr54 -
.expr33^(4/alpha)) * .expr33^(-5 + .expr34) * .expr31^.expr4/(E^.expr35 *
u1 * u2 * u3 * u4 * u5))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr37 <- -log(u6)
.expr39 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr37^alpha
.expr40 <- 1/alpha
.expr41 <- .expr39^.expr40
.expr50 <- .expr39^(2/alpha)
.expr61 <- .expr39^(3/alpha)
.expr73 <- .expr39^(4/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * (.expr3 + 120 * alpha^5 +
274 * alpha^4 * (.expr3 + .expr41) + 225 * alpha^3 *
(1 - 3 * .expr41 + .expr50) + 85 * alpha^2 * (.expr3 +
7 * .expr41 - 6 * .expr50 + .expr61) + 15 * alpha * (1 -
15 * .expr41 + 25 * .expr50 - 10 * .expr61 + .expr73) +
31 * .expr41 - 90 * .expr50 + 65 * .expr61 - 15 * .expr73 +
.expr39^(5/alpha)) * .expr39^(-6 + .expr40) * .expr37^.expr4/(E^.expr41 *
u1 * u2 * u3 * u4 * u5 * u6)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr23 <- -log(u6)
.expr43 <- -log(u7)
.expr45 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr43^alpha
.expr46 <- 1/alpha
.expr47 <- .expr45^.expr46
.expr56 <- .expr45^(2/alpha)
.expr67 <- .expr45^(3/alpha)
.expr80 <- .expr45^(4/alpha)
.expr94 <- .expr45^(5/alpha)
.value <- -(.expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * (.expr3 -
720 * alpha^6 - 1764 * alpha^5 * (.expr3 + .expr47) -
1624 * alpha^4 * (1 - 3 * .expr47 + .expr56) - 735 *
alpha^3 * (.expr3 + 7 * .expr47 - 6 * .expr56 + .expr67) -
175 * alpha^2 * (1 - 15 * .expr47 + 25 * .expr56 - 10 *
.expr67 + .expr80) - 21 * alpha * (.expr3 + 31 *
.expr47 - 90 * .expr56 + 65 * .expr67 - 15 * .expr80 +
.expr94) + 63 * .expr47 - 301 * .expr56 + 350 * .expr67 -
140 * .expr80 + 21 * .expr94 - .expr45^(6/alpha)) * .expr45^(-7 +
.expr46) * .expr43^.expr4/(E^.expr47 * u1 * u2 * u3 *
u4 * u5 * u6 * u7))
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr23 <- -log(u6)
.expr27 <- -log(u7)
.expr49 <- -log(u8)
.expr51 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr49^alpha
.expr52 <- 1/alpha
.expr53 <- .expr51^.expr52
.expr62 <- .expr51^(2/alpha)
.expr73 <- .expr51^(3/alpha)
.expr86 <- .expr51^(4/alpha)
.expr101 <- .expr51^(5/alpha)
.expr117 <- .expr51^(6/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * .expr27^.expr4 *
(.expr3 + 5040 * alpha^7 + 13068 * alpha^6 * (.expr3 +
.expr53) + 13132 * alpha^5 * (1 - 3 * .expr53 + .expr62) +
6769 * alpha^4 * (.expr3 + 7 * .expr53 - 6 * .expr62 +
.expr73) + 1960 * alpha^3 * (1 - 15 * .expr53 +
25 * .expr62 - 10 * .expr73 + .expr86) + 322 * alpha^2 *
(.expr3 + 31 * .expr53 - 90 * .expr62 + 65 * .expr73 -
15 * .expr86 + .expr101) + 28 * alpha * (1 -
63 * .expr53 + 301 * .expr62 - 350 * .expr73 + 140 *
.expr86 - 21 * .expr101 + .expr117) + 127 * .expr53 -
966 * .expr62 + 1701 * .expr73 - 1050 * .expr86 +
266 * .expr101 - 28 * .expr117 + .expr51^(7/alpha)) *
.expr51^(-8 + .expr52) * .expr49^.expr4/(E^.expr53 *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr11 <- -log(u3)
.expr15 <- -log(u4)
.expr19 <- -log(u5)
.expr23 <- -log(u6)
.expr27 <- -log(u7)
.expr31 <- -log(u8)
.expr55 <- -log(u9)
.expr57 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr55^alpha
.expr58 <- 1/alpha
.expr59 <- .expr57^.expr58
.expr68 <- .expr57^(2/alpha)
.expr79 <- .expr57^(3/alpha)
.expr92 <- .expr57^(4/alpha)
.expr107 <- .expr57^(5/alpha)
.expr124 <- .expr57^(6/alpha)
.expr142 <- .expr57^(7/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * .expr27^.expr4 *
.expr31^.expr4 * (1 + 40320 * alpha^8 + 109584 * alpha^7 *
(.expr3 + .expr59) + 118124 * alpha^6 * (1 - 3 * .expr59 +
.expr68) + 67284 * alpha^5 * (.expr3 + 7 * .expr59 -
6 * .expr68 + .expr79) + 22449 * alpha^4 * (1 - 15 *
.expr59 + 25 * .expr68 - 10 * .expr79 + .expr92) + 4536 *
alpha^3 * (.expr3 + 31 * .expr59 - 90 * .expr68 + 65 *
.expr79 - 15 * .expr92 + .expr107) + 546 * alpha^2 *
(1 - 63 * .expr59 + 301 * .expr68 - 350 * .expr79 + 140 *
.expr92 - 21 * .expr107 + .expr124) + 36 * alpha *
(.expr3 + 127 * .expr59 - 966 * .expr68 + 1701 * .expr79 -
1050 * .expr92 + 266 * .expr107 - 28 * .expr124 +
.expr142) - 255 * .expr59 + 3025 * .expr68 - 7770 *
.expr79 + 6951 * .expr92 - 2646 * .expr107 + 462 * .expr124 -
36 * .expr142 + .expr57^(8/alpha)) * .expr57^(-9 + .expr58) *
.expr55^.expr4/(E^.expr59 * u1 * u2 * u3 * u4 * u5 *
u6 * u7 * u8 * u9)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u10)
.expr11 <- -log(u2)
.expr15 <- -log(u3)
.expr19 <- -log(u4)
.expr23 <- -log(u5)
.expr27 <- -log(u6)
.expr31 <- -log(u7)
.expr35 <- -log(u8)
.expr61 <- -log(u9)
.expr63 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr35^alpha + .expr61^alpha
.expr64 <- 1/alpha
.expr65 <- .expr63^.expr64
.expr74 <- .expr63^(2/alpha)
.expr85 <- .expr63^(3/alpha)
.expr98 <- .expr63^(4/alpha)
.expr113 <- .expr63^(5/alpha)
.expr130 <- .expr63^(6/alpha)
.expr149 <- .expr63^(7/alpha)
.expr169 <- .expr63^(8/alpha)
.value <- .expr2^.expr4 * .expr7^.expr4 * .expr11^.expr4 *
.expr15^.expr4 * .expr19^.expr4 * .expr23^.expr4 * .expr27^.expr4 *
.expr31^.expr4 * .expr35^.expr4 * (.expr3 + 362880 *
alpha^9 + 1026576 * alpha^8 * (.expr3 + .expr65) + 1172700 *
alpha^7 * (1 - 3 * .expr65 + .expr74) + 723680 * alpha^6 *
(.expr3 + 7 * .expr65 - 6 * .expr74 + .expr85) + 269325 *
alpha^5 * (1 - 15 * .expr65 + 25 * .expr74 - 10 * .expr85 +
.expr98) + 63273 * alpha^4 * (.expr3 + 31 * .expr65 -
90 * .expr74 + 65 * .expr85 - 15 * .expr98 + .expr113) +
9450 * alpha^3 * (1 - 63 * .expr65 + 301 * .expr74 -
350 * .expr85 + 140 * .expr98 - 21 * .expr113 + .expr130) +
870 * alpha^2 * (.expr3 + 127 * .expr65 - 966 * .expr74 +
1701 * .expr85 - 1050 * .expr98 + 266 * .expr113 -
28 * .expr130 + .expr149) + 45 * alpha * (1 - 255 *
.expr65 + 3025 * .expr74 - 7770 * .expr85 + 6951 * .expr98 -
2646 * .expr113 + 462 * .expr130 - 36 * .expr149 + .expr169) +
511 * .expr65 - 9330 * .expr74 + 34105 * .expr85 - 42525 *
.expr98 + 22827 * .expr113 - 5880 * .expr130 + 750 *
.expr149 - 45 * .expr169 + .expr63^(9/alpha)) * .expr63^(-10 +
.expr64) * .expr61^.expr4/(E^.expr65 * u1 * u10 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.pdfDerWrtArg.expr` <-
expression(((-log(u1))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1)) + ((-log(u1))^alpha)^(1/alpha) * ((E^((-log(u1))^alpha)^(1/alpha) -
E^((-log(u1))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * log(u1) + E^((-log(u1))^alpha)^(1/alpha) *
u1 * (1/u1))/(E^((-log(u1))^alpha)^(1/alpha) * u1 * log(u1))^2,
-(((-log(u1))^(-1 + alpha) * (-1 + alpha + ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)) * (((-log(u1))^alpha + (-log(u2))^alpha)^((-2 +
1/alpha) - 1) * ((-2 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + ((-log(u1))^(-1 + alpha) *
(((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
(-log(u1))^((-1 + alpha) - 1) * ((-1 + alpha) * (1/u1)) *
(-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha)^(-2 + 1/alpha)) *
(-log(u2))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
u1 * u2) + ((-log(u1))^(-1 + alpha) * (-1 + alpha + ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha)^(-2 +
1/alpha) * (-log(u2))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) - E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2)/(E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
u1 * u2)^2), -(((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((-3 +
1/alpha) - 1) * ((-3 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))) + (3 * alpha * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
3 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (1 + 2 *
alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha))) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(-3 + 1/alpha)) *
(-log(u3))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * u1 * u2 * u3) + ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (1 + 2 * alpha^2 +
3 * alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(-3 + 1/alpha) *
(-log(u3))^(-1 + alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) - E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * u1 * u2 * u3)^2), (((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(6 * alpha * (3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 11 * alpha^2 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(-4 + 1/alpha) - (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((-4 + 1/alpha) - 1) * ((-4 + 1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
(-log(u4))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 +
11 * alpha^2 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(-4 + 1/alpha) * (-log(u4))^(-1 +
alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3 * u4)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4)^2, -((((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(50 * alpha^3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 35 * alpha^2 * (3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 10 *
alpha * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 -
50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) -
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 -
50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((-5 + 1/alpha) -
1) * ((-5 + 1/alpha) * ((-log(u1))^(alpha - 1) *
(alpha * (1/u1)))))) * (-log(u5))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5) -
((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-1 - 24 * alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) - 35 * alpha^2 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) *
(-log(u5))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3 * u4 * u5)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5)^2), (((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (225 * alpha^3 * (3 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 274 * alpha^4 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
85 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))) + (7 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
15 * alpha * (15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 25 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 90 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) - 1) *
((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
65 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - (-log(u1))^((-1 + alpha) -
1) * ((-1 + alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-1 + 120 * alpha^5 + 274 * alpha^4 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 + 274 *
alpha^4 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((-6 +
1/alpha) - 1) * ((-6 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))))) * (-log(u6))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 +
274 * alpha^4 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) * (-log(u6))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2 * u3 * u4 * u5 * u6)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6)^2, -((((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(1764 * alpha^5 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 1624 * alpha^4 * (3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 735 * alpha^3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) - 175 * alpha^2 * (15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 21 * alpha * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) - 63 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 301 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 350 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 140 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 21 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-1 - 720 * alpha^6 - 1764 *
alpha^5 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) - 1624 *
alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha))) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(-7 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-1 -
720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) - 175 * alpha^2 *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha)) -
21 * alpha * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(6/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((-7 + 1/alpha) - 1) * ((-7 + 1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
(-log(u7))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6 * u7) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-1 - 720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha *
(-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(6/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(-7 + 1/alpha) * (-log(u7))^(-1 +
alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
u1) * u2 * u3 * u4 * u5 * u6 * u7)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7)^2), (((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (13132 * alpha^5 *
(3 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 13068 * alpha^6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 6769 * alpha^4 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 1960 * alpha^3 * (15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 25 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 10 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 322 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 28 * alpha * (63 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 301 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 350 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - 140 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) + 21 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 127 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 966 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 1701 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 1050 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 266 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 28 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((7/alpha) - 1) *
((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
(-log(u1))^((-1 + alpha) - 1) * ((-1 + alpha) * (1/u1)) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha)) + 1960 * alpha^3 *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha)) + 28 * alpha *
(1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) -
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-1 + 5040 * alpha^7 + 13068 * alpha^6 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) +
13132 * alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((-8 + 1/alpha) -
1) * ((-8 + 1/alpha) * ((-log(u1))^(alpha - 1) *
(alpha * (1/u1)))))) * (-log(u8))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 *
u6 * u7 * u8) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) +
13132 * alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
(-log(u8))^(-1 + alpha)) * ((E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2 * u3 * u4 * u5 * u6 *
u7 * u8)/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6 * u7 * u8)^2, (((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(118124 * alpha^6 * (3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 109584 * alpha^7 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 67284 * alpha^5 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 6 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 22449 * alpha^4 * (15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 10 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 4536 *
alpha^3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))) + (65 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 90 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
546 * alpha^2 * (63 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
301 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
350 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
140 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
21 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) *
(alpha * (1/u1))))) - 36 * alpha * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (266 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + (1701 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + (127 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 966 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) - 1050 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
28 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))))) + 255 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 3025 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 7770 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 6951 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 2646 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 462 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 36 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((7/alpha) - 1) * ((7/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) -
1) * ((8/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 +
alpha) * (1/u1)) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 +
alpha) * (1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
118124 * alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (1 + 40320 * alpha^8 +
109584 * alpha^7 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 118124 * alpha^6 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((-9 +
1/alpha) - 1) * ((-9 + 1/alpha) * ((-log(u1))^(alpha -
1) * (alpha * (1/u1)))))) * (-log(u9))^(-1 + alpha)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 *
u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
118124 * alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * (-log(u9))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u2 * u3 * u4 * u5 * u6 * u7 *
u8 * u9)/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)^2, (((-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (1172700 * alpha^7 *
(3 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 1026576 * alpha^8 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 723680 * alpha^6 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (7 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
6 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
269325 * alpha^5 * (15 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 25 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 10 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 63273 * alpha^4 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (65 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
(31 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 90 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
15 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
9450 * alpha^3 * (63 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 301 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 350 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 140 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 21 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 870 * alpha^2 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))) + (266 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) - 1) *
((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
(1701 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + (127 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) -
966 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
1050 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) -
28 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))))) +
45 * alpha * (255 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 3025 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 7770 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 6951 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 2646 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 462 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) + 36 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) -
1) * ((8/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - 511 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) +
9330 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 34105 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 42525 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 22827 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 5880 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - 750 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((7/alpha) - 1) * ((7/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) + 45 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((8/alpha) - 1) * ((8/alpha) *
((-log(u1))^(alpha - 1) * (alpha * (1/u1))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((9/alpha) -
1) * ((9/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1))))) - (-log(u1))^((-1 + alpha) - 1) * ((-1 + alpha) *
(1/u1)) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 +
1026576 * alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
1172700 * alpha^7 * (1 - 3 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 723680 * alpha^6 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 *
(1 - 15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
63273 * alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
9450 * alpha^3 * (1 - 63 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 350 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) - 21 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) +
511 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 9330 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
34105 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 42525 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
22827 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 5880 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
750 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) - 45 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(9/alpha))) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) - (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(-1 + 362880 * alpha^9 + 1026576 * alpha^8 * (-1 + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
1172700 * alpha^7 * (1 - 3 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 723680 * alpha^6 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
269325 * alpha^5 * (1 - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 63273 * alpha^4 *
(-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 *
(1 - 63 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha *
(1 - 255 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((-10 + 1/alpha) - 1) * ((-10 +
1/alpha) * ((-log(u1))^(alpha - 1) * (alpha * (1/u1)))))) *
(-log(u9))^(-1 + alpha)/(E^((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 *
u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 +
1026576 * alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
1172700 * alpha^7 * (1 - 3 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 723680 * alpha^6 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 *
(1 - 15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
63273 * alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
9450 * alpha^3 * (1 - 63 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 350 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) - 21 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) +
511 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 9330 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
34105 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 42525 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
22827 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 5880 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
750 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) - 45 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * (-log(u9))^(-1 + alpha)) * ((E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
E^((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^(alpha - 1) * (alpha *
(1/u1)))))) * u1) * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9)/(E^((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 *
u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)^2)
`gumbelCopula.pdfDerWrtArg.algr` <-
expression({
.expr1 <- log(u1)
.expr2 <- -.expr1
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.expr9 <- 1/u1
.expr13 <- .expr3^(.expr4 - 1) * (.expr4 * (.expr2^(alpha -
1) * (alpha * .expr9)))
.expr14 <- .expr3^.expr4
.expr15 <- E^.expr14
.expr16 <- .expr15 * u1
.expr17 <- .expr16 * .expr1
.value <- .expr13/.expr17 + .expr14 * ((.expr15 - .expr15 *
(log(E) * .expr13) * u1) * .expr1 + .expr16 * .expr9)/.expr17^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr4 <- -1 + alpha
.expr5 <- .expr2^.expr4
.expr8 <- -log(u2)
.expr10 <- .expr2^alpha + .expr8^alpha
.expr11 <- 1/alpha
.expr12 <- .expr10^.expr11
.expr13 <- .expr4 + .expr12
.expr14 <- .expr5 * .expr13
.expr16 <- -2 + .expr11
.expr21 <- 1/u1
.expr23 <- .expr2^(alpha - 1) * (alpha * .expr21)
.expr30 <- .expr10^(.expr11 - 1) * (.expr11 * .expr23)
.expr38 <- .expr10^.expr16
.expr41 <- .expr8^.expr4
.expr43 <- E^.expr12
.expr45 <- .expr43 * u1 * u2
.value <- -((.expr14 * (.expr10^(.expr16 - 1) * (.expr16 *
.expr23)) + (.expr5 * .expr30 + .expr2^(.expr4 - 1) *
(.expr4 * .expr21) * .expr13) * .expr38) * .expr41/.expr45 +
.expr14 * .expr38 * .expr41 * ((.expr43 - .expr43 * (log(E) *
.expr30) * u1) * u2)/.expr45^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr9 <- .expr2^.expr4 * .expr8
.expr13 <- 3 * alpha
.expr18 <- -log(u3)
.expr20 <- .expr2^alpha + .expr7^alpha + .expr18^alpha
.expr21 <- 1/alpha
.expr22 <- .expr20^.expr21
.expr28 <- 2/alpha
.expr30 <- 1 + 2 * alpha^2 + .expr13 * (.expr3 + .expr22) -
3 * .expr22 + .expr20^.expr28
.expr31 <- .expr9 * .expr30
.expr33 <- -3 + .expr21
.expr38 <- 1/u1
.expr40 <- .expr2^(alpha - 1) * (alpha * .expr38)
.expr51 <- .expr20^(.expr21 - 1) * (.expr21 * .expr40)
.expr64 <- .expr20^.expr33
.expr67 <- .expr18^.expr4
.expr69 <- E^.expr22
.expr72 <- .expr69 * u1 * u2 * u3
.value <- -((.expr31 * (.expr20^(.expr33 - 1) * (.expr33 *
.expr40)) + (.expr9 * (.expr20^(.expr28 - 1) * (.expr28 *
.expr40) + (.expr13 * .expr51 - 3 * .expr51)) + .expr2^(.expr4 -
1) * (.expr4 * .expr38) * .expr8 * .expr30) * .expr64) *
.expr67/.expr72 + .expr31 * .expr64 * .expr67 * ((.expr69 -
.expr69 * (log(E) * .expr51) * u1) * u2 * u3)/.expr72^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr13 <- .expr2^.expr4 * .expr8 * .expr12
.expr14 <- 6 * alpha
.expr21 <- -log(u4)
.expr23 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr21^alpha
.expr24 <- 1/alpha
.expr29 <- 1/u1
.expr31 <- .expr2^(alpha - 1) * (alpha * .expr29)
.expr33 <- .expr23^(.expr24 - 1) * (.expr24 * .expr31)
.expr35 <- 2/alpha
.expr39 <- .expr23^(.expr35 - 1) * (.expr35 * .expr31)
.expr43 <- 11 * alpha^2
.expr50 <- 3/alpha
.expr66 <- .expr23^.expr24
.expr72 <- .expr23^.expr35
.expr81 <- .expr3 + 6 * alpha^3 + .expr43 * (.expr3 + .expr66) +
.expr14 * (1 - 3 * .expr66 + .expr72) + 7 * .expr66 -
6 * .expr72 + .expr23^.expr50
.expr85 <- -4 + .expr24
.expr86 <- .expr23^.expr85
.expr88 <- .expr13 * .expr81
.expr95 <- .expr21^.expr4
.expr97 <- E^.expr66
.expr101 <- .expr97 * u1 * u2 * u3 * u4
.value <- ((.expr13 * (.expr14 * (3 * .expr33 - .expr39) -
.expr43 * .expr33 - 7 * .expr33 + 6 * .expr39 - .expr23^(.expr50 -
1) * (.expr50 * .expr31)) - .expr2^(.expr4 - 1) * (.expr4 *
.expr29) * .expr8 * .expr12 * .expr81) * .expr86 - .expr88 *
(.expr23^(.expr85 - 1) * (.expr85 * .expr31))) * .expr95/.expr101 -
.expr88 * .expr86 * .expr95 * ((.expr97 - .expr97 * (log(E) *
.expr33) * u1) * u2 * u3 * u4)/.expr101^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr17 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16
.expr19 <- 50 * alpha^3
.expr28 <- -log(u5)
.expr30 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr28^alpha
.expr31 <- 1/alpha
.expr36 <- 1/u1
.expr38 <- .expr2^(alpha - 1) * (alpha * .expr36)
.expr40 <- .expr30^(.expr31 - 1) * (.expr31 * .expr38)
.expr43 <- 35 * alpha^2
.expr45 <- 2/alpha
.expr49 <- .expr30^(.expr45 - 1) * (.expr45 * .expr38)
.expr53 <- 10 * alpha
.expr54 <- 3/alpha
.expr58 <- .expr30^(.expr54 - 1) * (.expr54 * .expr38)
.expr71 <- 4/alpha
.expr88 <- .expr30^.expr31
.expr94 <- .expr30^.expr45
.expr102 <- .expr30^.expr54
.expr113 <- .expr3 - 24 * alpha^4 - .expr19 * (.expr3 + .expr88) -
.expr43 * (1 - 3 * .expr88 + .expr94) - .expr53 * (.expr3 +
7 * .expr88 - 6 * .expr94 + .expr102) + 15 * .expr88 -
25 * .expr94 + 10 * .expr102 - .expr30^.expr71
.expr117 <- -5 + .expr31
.expr118 <- .expr30^.expr117
.expr120 <- .expr17 * .expr113
.expr127 <- .expr28^.expr4
.expr129 <- E^.expr88
.expr134 <- .expr129 * u1 * u2 * u3 * u4 * u5
.value <- -(((.expr17 * (.expr19 * .expr40 - .expr43 * (3 *
.expr40 - .expr49) + .expr53 * (.expr58 + (7 * .expr40 -
6 * .expr49)) - 15 * .expr40 + 25 * .expr49 - 10 * .expr58 +
.expr30^(.expr71 - 1) * (.expr71 * .expr38)) - .expr2^(.expr4 -
1) * (.expr4 * .expr36) * .expr8 * .expr12 * .expr16 *
.expr113) * .expr118 - .expr120 * (.expr30^(.expr117 -
1) * (.expr117 * .expr38))) * .expr127/.expr134 - .expr120 *
.expr118 * .expr127 * ((.expr129 - .expr129 * (log(E) *
.expr40) * u1) * u2 * u3 * u4 * u5)/.expr134^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr21 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20
.expr23 <- 225 * alpha^3
.expr34 <- -log(u6)
.expr36 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr34^alpha
.expr37 <- 1/alpha
.expr42 <- 1/u1
.expr44 <- .expr2^(alpha - 1) * (alpha * .expr42)
.expr46 <- .expr36^(.expr37 - 1) * (.expr37 * .expr44)
.expr48 <- 2/alpha
.expr52 <- .expr36^(.expr48 - 1) * (.expr48 * .expr44)
.expr56 <- 274 * alpha^4
.expr60 <- 85 * alpha^2
.expr61 <- 3/alpha
.expr65 <- .expr36^(.expr61 - 1) * (.expr61 * .expr44)
.expr72 <- 15 * alpha
.expr78 <- 4/alpha
.expr82 <- .expr36^(.expr78 - 1) * (.expr78 * .expr44)
.expr94 <- 5/alpha
.expr112 <- .expr36^.expr37
.expr118 <- .expr36^.expr48
.expr126 <- .expr36^.expr61
.expr136 <- .expr36^.expr78
.expr149 <- .expr3 + 120 * alpha^5 + .expr56 * (.expr3 +
.expr112) + .expr23 * (1 - 3 * .expr112 + .expr118) +
.expr60 * (.expr3 + 7 * .expr112 - 6 * .expr118 + .expr126) +
.expr72 * (1 - 15 * .expr112 + 25 * .expr118 - 10 * .expr126 +
.expr136) + 31 * .expr112 - 90 * .expr118 + 65 *
.expr126 - 15 * .expr136 + .expr36^.expr94
.expr153 <- -6 + .expr37
.expr154 <- .expr36^.expr153
.expr156 <- .expr21 * .expr149
.expr163 <- .expr34^.expr4
.expr165 <- E^.expr112
.expr171 <- .expr165 * u1 * u2 * u3 * u4 * u5 * u6
.value <- ((.expr21 * (.expr23 * (3 * .expr46 - .expr52) -
.expr56 * .expr46 - .expr60 * (.expr65 + (7 * .expr46 -
6 * .expr52)) + .expr72 * (15 * .expr46 - 25 * .expr52 +
10 * .expr65 - .expr82) - 31 * .expr46 + 90 * .expr52 -
65 * .expr65 + 15 * .expr82 - .expr36^(.expr94 - 1) *
(.expr94 * .expr44)) - .expr2^(.expr4 - 1) * (.expr4 *
.expr42) * .expr8 * .expr12 * .expr16 * .expr20 * .expr149) *
.expr154 - .expr156 * (.expr36^(.expr153 - 1) * (.expr153 *
.expr44))) * .expr163/.expr171 - .expr156 * .expr154 *
.expr163 * ((.expr165 - .expr165 * (log(E) * .expr46) *
u1) * u2 * u3 * u4 * u5 * u6)/.expr171^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u6)
.expr24 <- .expr23^.expr4
.expr25 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24
.expr27 <- 1764 * alpha^5
.expr40 <- -log(u7)
.expr42 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr40^alpha
.expr43 <- 1/alpha
.expr48 <- 1/u1
.expr50 <- .expr2^(alpha - 1) * (alpha * .expr48)
.expr52 <- .expr42^(.expr43 - 1) * (.expr43 * .expr50)
.expr55 <- 1624 * alpha^4
.expr57 <- 2/alpha
.expr61 <- .expr42^(.expr57 - 1) * (.expr57 * .expr50)
.expr66 <- 735 * alpha^3
.expr67 <- 3/alpha
.expr71 <- .expr42^(.expr67 - 1) * (.expr67 * .expr50)
.expr79 <- 175 * alpha^2
.expr85 <- 4/alpha
.expr89 <- .expr42^(.expr85 - 1) * (.expr85 * .expr50)
.expr93 <- 21 * alpha
.expr94 <- 5/alpha
.expr98 <- .expr42^(.expr94 - 1) * (.expr94 * .expr50)
.expr119 <- 6/alpha
.expr138 <- .expr42^.expr43
.expr144 <- .expr42^.expr57
.expr152 <- .expr42^.expr67
.expr162 <- .expr42^.expr85
.expr174 <- .expr42^.expr94
.expr189 <- .expr3 - 720 * alpha^6 - .expr27 * (.expr3 +
.expr138) - .expr55 * (1 - 3 * .expr138 + .expr144) -
.expr66 * (.expr3 + 7 * .expr138 - 6 * .expr144 + .expr152) -
.expr79 * (1 - 15 * .expr138 + 25 * .expr144 - 10 * .expr152 +
.expr162) - .expr93 * (.expr3 + 31 * .expr138 - 90 *
.expr144 + 65 * .expr152 - 15 * .expr162 + .expr174) +
63 * .expr138 - 301 * .expr144 + 350 * .expr152 - 140 *
.expr162 + 21 * .expr174 - .expr42^.expr119
.expr193 <- -7 + .expr43
.expr194 <- .expr42^.expr193
.expr196 <- .expr25 * .expr189
.expr203 <- .expr40^.expr4
.expr205 <- E^.expr138
.expr212 <- .expr205 * u1 * u2 * u3 * u4 * u5 * u6 * u7
.value <- -(((.expr25 * (.expr27 * .expr52 - .expr55 * (3 *
.expr52 - .expr61) + .expr66 * (.expr71 + (7 * .expr52 -
6 * .expr61)) - .expr79 * (15 * .expr52 - 25 * .expr61 +
10 * .expr71 - .expr89) + .expr93 * (.expr98 + (65 *
.expr71 + (31 * .expr52 - 90 * .expr61) - 15 * .expr89)) -
63 * .expr52 + 301 * .expr61 - 350 * .expr71 + 140 *
.expr89 - 21 * .expr98 + .expr42^(.expr119 - 1) * (.expr119 *
.expr50)) - .expr2^(.expr4 - 1) * (.expr4 * .expr48) *
.expr8 * .expr12 * .expr16 * .expr20 * .expr24 * .expr189) *
.expr194 - .expr196 * (.expr42^(.expr193 - 1) * (.expr193 *
.expr50))) * .expr203/.expr212 - .expr196 * .expr194 *
.expr203 * ((.expr205 - .expr205 * (log(E) * .expr52) *
u1) * u2 * u3 * u4 * u5 * u6 * u7)/.expr212^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u6)
.expr24 <- .expr23^.expr4
.expr27 <- -log(u7)
.expr28 <- .expr27^.expr4
.expr29 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24 * .expr28
.expr31 <- 13132 * alpha^5
.expr46 <- -log(u8)
.expr48 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr46^alpha
.expr49 <- 1/alpha
.expr54 <- 1/u1
.expr56 <- .expr2^(alpha - 1) * (alpha * .expr54)
.expr58 <- .expr48^(.expr49 - 1) * (.expr49 * .expr56)
.expr60 <- 2/alpha
.expr64 <- .expr48^(.expr60 - 1) * (.expr60 * .expr56)
.expr68 <- 13068 * alpha^6
.expr72 <- 6769 * alpha^4
.expr73 <- 3/alpha
.expr77 <- .expr48^(.expr73 - 1) * (.expr73 * .expr56)
.expr85 <- 1960 * alpha^3
.expr91 <- 4/alpha
.expr95 <- .expr48^(.expr91 - 1) * (.expr91 * .expr56)
.expr100 <- 322 * alpha^2
.expr101 <- 5/alpha
.expr105 <- .expr48^(.expr101 - 1) * (.expr101 * .expr56)
.expr116 <- 28 * alpha
.expr126 <- 6/alpha
.expr130 <- .expr48^(.expr126 - 1) * (.expr126 * .expr56)
.expr146 <- 7/alpha
.expr166 <- .expr48^.expr49
.expr172 <- .expr48^.expr60
.expr180 <- .expr48^.expr73
.expr190 <- .expr48^.expr91
.expr202 <- .expr48^.expr101
.expr216 <- .expr48^.expr126
.expr233 <- .expr3 + 5040 * alpha^7 + .expr68 * (.expr3 +
.expr166) + .expr31 * (1 - 3 * .expr166 + .expr172) +
.expr72 * (.expr3 + 7 * .expr166 - 6 * .expr172 + .expr180) +
.expr85 * (1 - 15 * .expr166 + 25 * .expr172 - 10 * .expr180 +
.expr190) + .expr100 * (.expr3 + 31 * .expr166 -
90 * .expr172 + 65 * .expr180 - 15 * .expr190 + .expr202) +
.expr116 * (1 - 63 * .expr166 + 301 * .expr172 - 350 *
.expr180 + 140 * .expr190 - 21 * .expr202 + .expr216) +
127 * .expr166 - 966 * .expr172 + 1701 * .expr180 - 1050 *
.expr190 + 266 * .expr202 - 28 * .expr216 + .expr48^.expr146
.expr237 <- -8 + .expr49
.expr238 <- .expr48^.expr237
.expr240 <- .expr29 * .expr233
.expr247 <- .expr46^.expr4
.expr249 <- E^.expr166
.expr257 <- .expr249 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8
.value <- ((.expr29 * (.expr31 * (3 * .expr58 - .expr64) -
.expr68 * .expr58 - .expr72 * (.expr77 + (7 * .expr58 -
6 * .expr64)) + .expr85 * (15 * .expr58 - 25 * .expr64 +
10 * .expr77 - .expr95) - .expr100 * (.expr105 + (65 *
.expr77 + (31 * .expr58 - 90 * .expr64) - 15 * .expr95)) +
.expr116 * (63 * .expr58 - 301 * .expr64 + 350 * .expr77 -
140 * .expr95 + 21 * .expr105 - .expr130) - 127 *
.expr58 + 966 * .expr64 - 1701 * .expr77 + 1050 * .expr95 -
266 * .expr105 + 28 * .expr130 - .expr48^(.expr146 -
1) * (.expr146 * .expr56)) - .expr2^(.expr4 - 1) * (.expr4 *
.expr54) * .expr8 * .expr12 * .expr16 * .expr20 * .expr24 *
.expr28 * .expr233) * .expr238 - .expr240 * (.expr48^(.expr237 -
1) * (.expr237 * .expr56))) * .expr247/.expr257 - .expr240 *
.expr238 * .expr247 * ((.expr249 - .expr249 * (log(E) *
.expr58) * u1) * u2 * u3 * u4 * u5 * u6 * u7 * u8)/.expr257^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u2)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u3)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u4)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u5)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u6)
.expr24 <- .expr23^.expr4
.expr27 <- -log(u7)
.expr28 <- .expr27^.expr4
.expr31 <- -log(u8)
.expr32 <- .expr31^.expr4
.expr33 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24 * .expr28 * .expr32
.expr35 <- 118124 * alpha^6
.expr52 <- -log(u9)
.expr54 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr52^alpha
.expr55 <- 1/alpha
.expr60 <- 1/u1
.expr62 <- .expr2^(alpha - 1) * (alpha * .expr60)
.expr64 <- .expr54^(.expr55 - 1) * (.expr55 * .expr62)
.expr66 <- 2/alpha
.expr70 <- .expr54^(.expr66 - 1) * (.expr66 * .expr62)
.expr74 <- 109584 * alpha^7
.expr78 <- 67284 * alpha^5
.expr79 <- 3/alpha
.expr83 <- .expr54^(.expr79 - 1) * (.expr79 * .expr62)
.expr91 <- 22449 * alpha^4
.expr97 <- 4/alpha
.expr101 <- .expr54^(.expr97 - 1) * (.expr97 * .expr62)
.expr106 <- 4536 * alpha^3
.expr107 <- 5/alpha
.expr111 <- .expr54^(.expr107 - 1) * (.expr107 * .expr62)
.expr123 <- 546 * alpha^2
.expr133 <- 6/alpha
.expr137 <- .expr54^(.expr133 - 1) * (.expr133 * .expr62)
.expr141 <- 36 * alpha
.expr142 <- 7/alpha
.expr146 <- .expr54^(.expr142 - 1) * (.expr142 * .expr62)
.expr175 <- 8/alpha
.expr196 <- .expr54^.expr55
.expr202 <- .expr54^.expr66
.expr210 <- .expr54^.expr79
.expr220 <- .expr54^.expr97
.expr232 <- .expr54^.expr107
.expr246 <- .expr54^.expr133
.expr262 <- .expr54^.expr142
.expr281 <- 1 + 40320 * alpha^8 + .expr74 * (.expr3 + .expr196) +
.expr35 * (1 - 3 * .expr196 + .expr202) + .expr78 * (.expr3 +
7 * .expr196 - 6 * .expr202 + .expr210) + .expr91 * (1 -
15 * .expr196 + 25 * .expr202 - 10 * .expr210 + .expr220) +
.expr106 * (.expr3 + 31 * .expr196 - 90 * .expr202 +
65 * .expr210 - 15 * .expr220 + .expr232) + .expr123 *
(1 - 63 * .expr196 + 301 * .expr202 - 350 * .expr210 +
140 * .expr220 - 21 * .expr232 + .expr246) + .expr141 *
(.expr3 + 127 * .expr196 - 966 * .expr202 + 1701 * .expr210 -
1050 * .expr220 + 266 * .expr232 - 28 * .expr246 +
.expr262) - 255 * .expr196 + 3025 * .expr202 - 7770 *
.expr210 + 6951 * .expr220 - 2646 * .expr232 + 462 *
.expr246 - 36 * .expr262 + .expr54^.expr175
.expr285 <- -9 + .expr55
.expr286 <- .expr54^.expr285
.expr288 <- .expr33 * .expr281
.expr295 <- .expr52^.expr4
.expr297 <- E^.expr196
.expr306 <- .expr297 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8 * u9
.value <- ((.expr33 * (.expr35 * (3 * .expr64 - .expr70) -
.expr74 * .expr64 - .expr78 * (.expr83 + (7 * .expr64 -
6 * .expr70)) + .expr91 * (15 * .expr64 - 25 * .expr70 +
10 * .expr83 - .expr101) - .expr106 * (.expr111 + (65 *
.expr83 + (31 * .expr64 - 90 * .expr70) - 15 * .expr101)) +
.expr123 * (63 * .expr64 - 301 * .expr70 + 350 * .expr83 -
140 * .expr101 + 21 * .expr111 - .expr137) - .expr141 *
(.expr146 + (266 * .expr111 + (1701 * .expr83 + (127 *
.expr64 - 966 * .expr70) - 1050 * .expr101) - 28 *
.expr137)) + 255 * .expr64 - 3025 * .expr70 + 7770 *
.expr83 - 6951 * .expr101 + 2646 * .expr111 - 462 * .expr137 +
36 * .expr146 - .expr54^(.expr175 - 1) * (.expr175 *
.expr62)) - .expr2^(.expr4 - 1) * (.expr4 * .expr60) *
.expr8 * .expr12 * .expr16 * .expr20 * .expr24 * .expr28 *
.expr32 * .expr281) * .expr286 - .expr288 * (.expr54^(.expr285 -
1) * (.expr285 * .expr62))) * .expr295/.expr306 - .expr288 *
.expr286 * .expr295 * ((.expr297 - .expr297 * (log(E) *
.expr64) * u1) * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)/.expr306^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr7 <- -log(u10)
.expr8 <- .expr7^.expr4
.expr11 <- -log(u2)
.expr12 <- .expr11^.expr4
.expr15 <- -log(u3)
.expr16 <- .expr15^.expr4
.expr19 <- -log(u4)
.expr20 <- .expr19^.expr4
.expr23 <- -log(u5)
.expr24 <- .expr23^.expr4
.expr27 <- -log(u6)
.expr28 <- .expr27^.expr4
.expr31 <- -log(u7)
.expr32 <- .expr31^.expr4
.expr35 <- -log(u8)
.expr36 <- .expr35^.expr4
.expr37 <- .expr2^.expr4 * .expr8 * .expr12 * .expr16 * .expr20 *
.expr24 * .expr28 * .expr32 * .expr36
.expr39 <- 1172700 * alpha^7
.expr58 <- -log(u9)
.expr60 <- .expr2^alpha + .expr7^alpha + .expr11^alpha +
.expr15^alpha + .expr19^alpha + .expr23^alpha + .expr27^alpha +
.expr31^alpha + .expr35^alpha + .expr58^alpha
.expr61 <- 1/alpha
.expr66 <- 1/u1
.expr68 <- .expr2^(alpha - 1) * (alpha * .expr66)
.expr70 <- .expr60^(.expr61 - 1) * (.expr61 * .expr68)
.expr72 <- 2/alpha
.expr76 <- .expr60^(.expr72 - 1) * (.expr72 * .expr68)
.expr80 <- 1026576 * alpha^8
.expr84 <- 723680 * alpha^6
.expr85 <- 3/alpha
.expr89 <- .expr60^(.expr85 - 1) * (.expr85 * .expr68)
.expr97 <- 269325 * alpha^5
.expr103 <- 4/alpha
.expr107 <- .expr60^(.expr103 - 1) * (.expr103 * .expr68)
.expr112 <- 63273 * alpha^4
.expr113 <- 5/alpha
.expr117 <- .expr60^(.expr113 - 1) * (.expr113 * .expr68)
.expr129 <- 9450 * alpha^3
.expr139 <- 6/alpha
.expr143 <- .expr60^(.expr139 - 1) * (.expr139 * .expr68)
.expr148 <- 870 * alpha^2
.expr149 <- 7/alpha
.expr153 <- .expr60^(.expr149 - 1) * (.expr149 * .expr68)
.expr168 <- 45 * alpha
.expr182 <- 8/alpha
.expr186 <- .expr60^(.expr182 - 1) * (.expr182 * .expr68)
.expr206 <- 9/alpha
.expr228 <- .expr60^.expr61
.expr234 <- .expr60^.expr72
.expr242 <- .expr60^.expr85
.expr252 <- .expr60^.expr103
.expr264 <- .expr60^.expr113
.expr278 <- .expr60^.expr139
.expr294 <- .expr60^.expr149
.expr312 <- .expr60^.expr182
.expr333 <- .expr3 + 362880 * alpha^9 + .expr80 * (.expr3 +
.expr228) + .expr39 * (1 - 3 * .expr228 + .expr234) +
.expr84 * (.expr3 + 7 * .expr228 - 6 * .expr234 + .expr242) +
.expr97 * (1 - 15 * .expr228 + 25 * .expr234 - 10 * .expr242 +
.expr252) + .expr112 * (.expr3 + 31 * .expr228 -
90 * .expr234 + 65 * .expr242 - 15 * .expr252 + .expr264) +
.expr129 * (1 - 63 * .expr228 + 301 * .expr234 - 350 *
.expr242 + 140 * .expr252 - 21 * .expr264 + .expr278) +
.expr148 * (.expr3 + 127 * .expr228 - 966 * .expr234 +
1701 * .expr242 - 1050 * .expr252 + 266 * .expr264 -
28 * .expr278 + .expr294) + .expr168 * (1 - 255 *
.expr228 + 3025 * .expr234 - 7770 * .expr242 + 6951 *
.expr252 - 2646 * .expr264 + 462 * .expr278 - 36 * .expr294 +
.expr312) + 511 * .expr228 - 9330 * .expr234 + 34105 *
.expr242 - 42525 * .expr252 + 22827 * .expr264 - 5880 *
.expr278 + 750 * .expr294 - 45 * .expr312 + .expr60^.expr206
.expr337 <- -10 + .expr61
.expr338 <- .expr60^.expr337
.expr340 <- .expr37 * .expr333
.expr347 <- .expr58^.expr4
.expr349 <- E^.expr228
.expr359 <- .expr349 * u1 * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9
.value <- ((.expr37 * (.expr39 * (3 * .expr70 - .expr76) -
.expr80 * .expr70 - .expr84 * (.expr89 + (7 * .expr70 -
6 * .expr76)) + .expr97 * (15 * .expr70 - 25 * .expr76 +
10 * .expr89 - .expr107) - .expr112 * (.expr117 + (65 *
.expr89 + (31 * .expr70 - 90 * .expr76) - 15 * .expr107)) +
.expr129 * (63 * .expr70 - 301 * .expr76 + 350 * .expr89 -
140 * .expr107 + 21 * .expr117 - .expr143) - .expr148 *
(.expr153 + (266 * .expr117 + (1701 * .expr89 + (127 *
.expr70 - 966 * .expr76) - 1050 * .expr107) - 28 *
.expr143)) + .expr168 * (255 * .expr70 - 3025 * .expr76 +
7770 * .expr89 - 6951 * .expr107 + 2646 * .expr117 -
462 * .expr143 + 36 * .expr153 - .expr186) - 511 * .expr70 +
9330 * .expr76 - 34105 * .expr89 + 42525 * .expr107 -
22827 * .expr117 + 5880 * .expr143 - 750 * .expr153 +
45 * .expr186 - .expr60^(.expr206 - 1) * (.expr206 *
.expr68)) - .expr2^(.expr4 - 1) * (.expr4 * .expr66) *
.expr8 * .expr12 * .expr16 * .expr20 * .expr24 * .expr28 *
.expr32 * .expr36 * .expr333) * .expr338 - .expr340 *
(.expr60^(.expr337 - 1) * (.expr337 * .expr68))) * .expr347/.expr359 -
.expr340 * .expr338 * .expr347 * ((.expr349 - .expr349 *
(log(E) * .expr70) * u1) * u10 * u2 * u3 * u4 * u5 *
u6 * u7 * u8 * u9)/.expr359^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.pdfDerWrtPar.expr` <-
expression(-((((-log(u1))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))))) - ((-log(u1))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha)) * (1/alpha^2)))/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1)) - ((-log(u1))^alpha)^(1/alpha) * (E^((-log(u1))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))))) - ((-log(u1))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha)) * (1/alpha^2)))) * u1 * log(u1))/(E^((-log(u1))^alpha)^(1/alpha) *
u1 * log(u1))^2), ((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) +
(-log(u1))^(-1 + alpha) * (1 + (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2))))) * ((-log(u1))^alpha +
(-log(u2))^alpha)^(-2 + 1/alpha) + (-log(u1))^(-1 + alpha) *
(-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha)^((-2 + 1/alpha) -
1) * ((-2 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(-2 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2)))) * (-log(u2))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-1 + alpha + ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha)^(-2 +
1/alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * u1 * u2) - ((-log(u1))^(-1 +
alpha) * (-1 + alpha + ((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha)^(-2 + 1/alpha) * (-log(u2))^(-1 +
alpha)) * (E^((-log(u1))^alpha + (-log(u2))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))))) - ((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha)) * (1/alpha^2)))) * u1 * u2)/(E^((-log(u1))^alpha +
(-log(u2))^alpha)^(1/alpha) * u1 * u2)^2, (((((-log(u1))^(-1 +
alpha) * log((-log(u1))) * (-log(u2))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (1 +
2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(2/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (2 * (2 * alpha) + (3 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) + 3 * alpha *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2)))) -
3 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (2/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^((-3 + 1/alpha) - 1) *
((-3 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * (log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)) * (1/alpha^2)))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * ((-log(u3))^(-1 + alpha) * log((-log(u3)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) * u1 * u2 *
u3) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(1 + 2 * alpha^2 + 3 * alpha * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha)) - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(2/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(-3 +
1/alpha) * (-log(u3))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3)/(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha)^(1/alpha) *
u1 * u2 * u3)^2, ((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(6 * (3 * alpha^2) + (11 * (2 * alpha) * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
11 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2)))) + (6 * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 6 * alpha * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)) * (1/alpha^2))))) + 7 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^((2/alpha) - 1) *
((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)) * (2/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(3/alpha^2))))) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(-4 + 1/alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-1 + 6 * alpha^3 + 11 * alpha^2 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha)) +
6 * alpha * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((-4 + 1/alpha) - 1) * ((-4 + 1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * (log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)) * (1/alpha^2)))) *
(-log(u4))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 + 11 *
alpha^2 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * ((-log(u4))^(-1 + alpha) * log((-log(u4)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-1 + 6 * alpha^3 + 11 *
alpha^2 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(1/alpha)) + 6 * alpha * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha)) + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^(2/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(3/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(-4 +
1/alpha) * (-log(u4))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)) *
(1/alpha^2)))) * u1 * u2 * u3 * u4)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4)^2, -((((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-log(u4))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-1 - 24 *
alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) - 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(4/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (15 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2))) -
(24 * (4 * alpha^3) + (50 * (3 * alpha^2) * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha)) + 50 * alpha^3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2)))) +
(35 * (2 * alpha) * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) +
35 * alpha^2 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (2/alpha^2)) - 3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2))))) +
(10 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
10 * alpha * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (1/alpha^2))) - 6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (2/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (3/alpha^2)))))) - 25 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((2/alpha) - 1) *
((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (2/alpha^2))) +
10 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (3/alpha^2))) -
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((4/alpha) - 1) *
((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (4/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(-5 + 1/alpha) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 -
50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(4/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^((-5 + 1/alpha) -
1) * ((-5 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(-5 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)) * (1/alpha^2)))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-1 -
24 * alpha^4 - 50 * alpha^3 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) -
35 * alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) -
10 * alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha)) +
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) - 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(4/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(-5 +
1/alpha) * ((-log(u5))^(-1 + alpha) * log((-log(u5)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5) - ((-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-1 - 24 * alpha^4 - 50 * alpha^3 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha)) - 35 *
alpha^2 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha)) - 10 *
alpha * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(3/alpha)) + 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) -
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(2/alpha) + 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)^(3/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(4/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(-5 +
1/alpha) * (-log(u5))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5)^2), ((((((((-log(u1))^(-1 + alpha) *
log((-log(u1))) * (-log(u2))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
((-log(u3))^(-1 + alpha) * log((-log(u3))))) * (-log(u4))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * ((-log(u4))^(-1 + alpha) * log((-log(u4))))) *
(-log(u5))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
((-log(u5))^(-1 + alpha) * log((-log(u5))))) * (-1 + 120 *
alpha^5 + 274 * alpha^4 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) + 85 * alpha^2 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(120 * (5 * alpha^4) + (274 * (4 * alpha^3) * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
274 * alpha^4 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (1/alpha^2)))) + (225 *
(3 * alpha^2) * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
225 * alpha^3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (2/alpha^2)) - 3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))))) +
(85 * (2 * alpha) * (-1 + 7 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
85 * alpha^2 * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (1/alpha^2))) - 6 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (2/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (3/alpha^2))))) +
(15 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
15 * alpha * (25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)) * (2/alpha^2))) - 15 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))) -
10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) *
(3/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (4/alpha^2))))) +
31 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2))) -
90 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (2/alpha^2))) +
65 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (3/alpha^2))) -
15 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (4/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (5/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-1 + 120 * alpha^5 + 274 * alpha^4 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha)) + 85 * alpha^2 * (-1 + 7 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((-6 +
1/alpha) - 1) * ((-6 + 1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(-6 + 1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)) *
(1/alpha^2)))) * (-log(u6))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-1 +
120 * alpha^5 + 274 * alpha^4 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) + 225 * alpha^3 *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) + 15 *
alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha)) + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(4/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(5/alpha)) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(-6 + 1/alpha) * ((-log(u6))^(-1 + alpha) *
log((-log(u6)))))/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6) -
((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-1 + 120 * alpha^5 + 274 * alpha^4 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha)) +
225 * alpha^3 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha)) +
85 * alpha^2 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha)) +
15 * alpha * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha)) +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(5/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^(-6 +
1/alpha) * (-log(u6))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5 * u6)/(E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 *
u6)^2, -((((((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-log(u4))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * ((-log(u5))^(-1 +
alpha) * log((-log(u5))))) * (-log(u6))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * ((-log(u6))^(-1 +
alpha) * log((-log(u6))))) * (-1 - 720 * alpha^6 - 1764 *
alpha^5 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) - 1624 * alpha^4 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) - 175 * alpha^2 * (1 -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha)) - 21 * alpha *
(-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(63 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))) - (720 * (6 * alpha^5) + (1764 * (5 * alpha^4) *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha)) + 1764 * alpha^5 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2)))) + (1624 * (4 * alpha^3) * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) +
1624 * alpha^4 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))))) + (735 * (3 * alpha^2) * (-1 +
7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) + 735 * alpha^3 * (7 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (1/alpha^2))) - 6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (3/alpha^2))))) + (175 * (2 *
alpha) * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) + 175 * alpha^2 * (25 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (2/alpha^2))) - 15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))) - 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (3/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(4/alpha^2))))) + (21 * (-1 + 31 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
21 * alpha * (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2))) + 65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(3/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(4/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(5/alpha^2)))))) - 301 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(2/alpha^2))) + 350 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((3/alpha) - 1) *
((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (3/alpha^2))) - 140 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(4/alpha^2))) + 21 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((5/alpha) - 1) *
((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (5/alpha^2))) - (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(6/alpha^2))))) * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(-7 + 1/alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-1 - 720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^((-7 + 1/alpha) - 1) *
((-7 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(-7 +
1/alpha) * (log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)) * (1/alpha^2)))) * (-log(u7))^(-1 + alpha) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-1 - 720 * alpha^6 - 1764 *
alpha^5 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) - 1624 *
alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha)) -
735 * alpha^3 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha)) -
175 * alpha^2 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha)) - 21 * alpha * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha)) + 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 350 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + 21 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(6/alpha)) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(-7 +
1/alpha) * ((-log(u7))^(-1 + alpha) * log((-log(u7)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-1 - 720 * alpha^6 - 1764 * alpha^5 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha)) -
1624 * alpha^4 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha)) - 735 * alpha^3 *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha)) - 175 * alpha^2 *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha)) -
21 * alpha * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(2/alpha) + 65 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(5/alpha)) +
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) - 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(2/alpha) +
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(3/alpha) - 140 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(4/alpha) +
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(5/alpha) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(6/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(-7 + 1/alpha) * (-log(u7))^(-1 + alpha)) *
(E^((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(E) * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)) *
(1/alpha^2)))) * u1 * u2 * u3 * u4 * u5 * u6 * u7)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha)^(1/alpha) *
u1 * u2 * u3 * u4 * u5 * u6 * u7)^2), ((((((((((-log(u1))^(-1 +
alpha) * log((-log(u1))) * (-log(u2))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
((-log(u3))^(-1 + alpha) * log((-log(u3))))) * (-log(u4))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * ((-log(u4))^(-1 + alpha) * log((-log(u4))))) *
(-log(u5))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
((-log(u5))^(-1 + alpha) * log((-log(u5))))) * (-log(u6))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * ((-log(u6))^(-1 + alpha) * log((-log(u6))))) * (-log(u7))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * ((-log(u7))^(-1 + alpha) *
log((-log(u7))))) * (-1 + 5040 * alpha^7 + 13068 * alpha^6 *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) + 13132 *
alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) + 6769 *
alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha)) + 1960 * alpha^3 * (1 - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha)) + 322 * alpha^2 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 90 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + 65 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha)) + 28 * alpha * (1 - 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + 140 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) - 21 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(6/alpha)) + 127 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 1050 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + 266 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) - 28 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(7/alpha)) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-log(u7))^(-1 + alpha) * (5040 * (7 * alpha^6) + (13068 *
(6 * alpha^5) * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) +
13068 * alpha^6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2)))) + (13132 * (5 * alpha^4) *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(2/alpha)) + 13132 * alpha^5 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2)) - 3 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))))) + (6769 * (4 * alpha^3) *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
6769 * alpha^4 * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 6 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (2/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))))) + (1960 * (3 *
alpha^2) * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha)) + 1960 * alpha^3 * (25 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2))) - 15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 10 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (4/alpha^2))))) + (322 * (2 * alpha) *
(-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 90 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
322 * alpha^2 * (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 90 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (2/alpha^2))) +
65 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) - 15 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (4/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (5/alpha^2))))) + (28 * (1 -
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + 301 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + 140 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) - 21 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(6/alpha)) + 28 * alpha * (301 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2))) - 63 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 350 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) + 140 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (4/alpha^2))) - 21 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (5/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((6/alpha) - 1) * ((6/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (6/alpha^2))))) + 127 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2))) - 966 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (2/alpha^2))) + 1701 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((3/alpha) - 1) * ((3/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (3/alpha^2))) - 1050 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((4/alpha) - 1) * ((4/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (4/alpha^2))) + 266 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((5/alpha) - 1) * ((5/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (5/alpha^2))) - 28 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((6/alpha) - 1) * ((6/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (6/alpha^2))) + (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^((7/alpha) - 1) * ((7/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (7/alpha^2))))) * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(-8 + 1/alpha) + (-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-log(u7))^(-1 + alpha) * (-1 + 5040 * alpha^7 + 13068 *
alpha^6 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha)) + 13132 *
alpha^5 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) + 6769 *
alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(3/alpha)) + 1960 * alpha^3 * (1 - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(4/alpha)) + 322 * alpha^2 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) - 90 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) + 65 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 15 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(5/alpha)) + 28 * alpha * (1 - 63 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) + 140 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) - 21 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(6/alpha)) + 127 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) - 1050 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) + 266 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) - 28 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(7/alpha)) * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^((-8 +
1/alpha) - 1) * ((-8 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(-8 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)) * (1/alpha^2)))) * (-log(u8))^(-1 + alpha) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-1 +
5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
((-log(u8))^(-1 + alpha) * log((-log(u8)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6 *
u7 * u8) - ((-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-1 + 5040 * alpha^7 + 13068 * alpha^6 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha)) + 13132 * alpha^5 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha)) +
6769 * alpha^4 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha)) +
1960 * alpha^3 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha)) +
322 * alpha^2 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha)) +
28 * alpha * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha)) +
127 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) -
966 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(7/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^(-8 + 1/alpha) *
(-log(u8))^(-1 + alpha)) * (E^((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha)^(1/alpha) * u1 * u2 * u3 * u4 * u5 * u6 *
u7 * u8)^2, (((((((((((-log(u1))^(-1 + alpha) * log((-log(u1))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * ((-log(u2))^(-1 +
alpha) * log((-log(u2))))) * (-log(u3))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) *
log((-log(u3))))) * (-log(u4))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * ((-log(u5))^(-1 +
alpha) * log((-log(u5))))) * (-log(u6))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * ((-log(u6))^(-1 +
alpha) * log((-log(u6))))) * (-log(u7))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * ((-log(u7))^(-1 + alpha) * log((-log(u7))))) * (-log(u8))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
((-log(u8))^(-1 + alpha) * log((-log(u8))))) * (1 + 40320 *
alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 118124 * alpha^6 * (1 - 3 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) + 22449 *
alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 4536 * alpha^3 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 1701 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) +
(-log(u1))^(-1 + alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 +
alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) *
(-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 +
alpha) * (40320 * (8 * alpha^7) + (109584 * (7 * alpha^6) *
(-1 + ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) +
109584 * alpha^7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) + (118124 * (6 * alpha^5) *
(1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
118124 * alpha^6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))))) + (67284 * (5 * alpha^4) *
(-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
67284 * alpha^5 * (7 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 6 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))))) + (22449 * (4 * alpha^3) *
(1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
22449 * alpha^4 * (25 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 10 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(4/alpha^2))))) + (4536 * (3 * alpha^2) * (-1 +
31 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
4536 * alpha^3 * (31 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 90 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) + 65 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(4/alpha^2))) + (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))))) + (546 * (2 * alpha) * (1 -
63 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
546 * alpha^2 * (301 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 63 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 350 * (((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (3/alpha^2))) +
140 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (4/alpha^2))) -
21 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (5/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (6/alpha^2))))) +
(36 * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) +
36 * alpha * (127 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 966 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (2/alpha^2))) +
1701 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((3/alpha) - 1) * ((3/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (3/alpha^2))) - 1050 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (4/alpha^2))) +
266 * (((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((5/alpha) - 1) * ((5/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (5/alpha^2))) - 28 *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (6/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (7/alpha^2))))) -
255 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (1/alpha^2))) +
3025 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) -
1) * ((2/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (2/alpha^2))) -
7770 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (3/alpha^2))) +
6951 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) -
1) * ((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (4/alpha^2))) -
2646 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (5/alpha^2))) +
462 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) -
1) * ((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (6/alpha^2))) -
36 * (((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (7/alpha^2))) +
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) -
1) * ((8/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (8/alpha^2))))) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) + (-log(u1))^(-1 + alpha) * (-log(u2))^(-1 +
alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) *
(-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 +
alpha) * (-log(u8))^(-1 + alpha) * (1 + 40320 * alpha^8 +
109584 * alpha^7 * (-1 + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 118124 * alpha^6 * (1 -
3 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
67284 * alpha^5 * (-1 + 7 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) + 22449 *
alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 4536 * alpha^3 * (-1 + 31 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
90 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 1701 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((-9 +
1/alpha) - 1) * ((-9 + 1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(-9 + 1/alpha) *
(log(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) * (-log(u9))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
(-log(u4))^(-1 + alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 +
alpha) * (-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) *
(1 + 40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 118124 *
alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 67284 * alpha^5 * (-1 +
7 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * ((-log(u9))^(-1 + alpha) * log((-log(u9)))))/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * (-log(u6))^(-1 + alpha) *
(-log(u7))^(-1 + alpha) * (-log(u8))^(-1 + alpha) * (1 +
40320 * alpha^8 + 109584 * alpha^7 * (-1 + ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 118124 *
alpha^6 * (1 - 3 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha)) + 67284 * alpha^5 * (-1 + 7 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
6 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
22449 * alpha^4 * (1 - 15 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 10 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) +
4536 * alpha^3 * (-1 + 31 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 65 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
15 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha)) +
546 * alpha^2 * (1 - 63 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) - 350 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) +
36 * alpha * (-1 + 127 * ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) + 1701 *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
1050 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
28 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha)) -
255 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
3025 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
6951 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
462 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) +
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) *
((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-9 +
1/alpha) * (-log(u9))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(E) *
(((-log(u1))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)) * (1/alpha^2)))) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)/(E^((-log(u1))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u2 *
u3 * u4 * u5 * u6 * u7 * u8 * u9)^2, ((((((((((((-log(u1))^(-1 +
alpha) * log((-log(u1))) * (-log(u10))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * ((-log(u10))^(-1 + alpha) * log((-log(u10))))) *
(-log(u2))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 +
alpha) * ((-log(u2))^(-1 + alpha) * log((-log(u2))))) * (-log(u3))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * ((-log(u3))^(-1 + alpha) * log((-log(u3))))) *
(-log(u4))^(-1 + alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 +
alpha) * (-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) *
((-log(u4))^(-1 + alpha) * log((-log(u4))))) * (-log(u5))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * ((-log(u5))^(-1 + alpha) * log((-log(u5))))) * (-log(u6))^(-1 +
alpha) + (-log(u1))^(-1 + alpha) * (-log(u10))^(-1 + alpha) *
(-log(u2))^(-1 + alpha) * (-log(u3))^(-1 + alpha) * (-log(u4))^(-1 +
alpha) * (-log(u5))^(-1 + alpha) * ((-log(u6))^(-1 + alpha) *
log((-log(u6))))) * (-log(u7))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * ((-log(u7))^(-1 + alpha) *
log((-log(u7))))) * (-log(u8))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
((-log(u8))^(-1 + alpha) * log((-log(u8))))) * (-1 + 362880 *
alpha^9 + 1026576 * alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 1172700 *
alpha^7 * (1 - 3 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) +
723680 * alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha)) +
269325 * alpha^5 * (1 - 15 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) + 25 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 63273 * alpha^4 *
(-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (362880 * (9 * alpha^8) + (1026576 *
(8 * alpha^7) * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha)) + 1026576 *
alpha^8 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) + (1172700 * (7 * alpha^6) * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 1172700 *
alpha^7 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2)) - 3 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))))) + (723680 * (6 *
alpha^5) * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 723680 * alpha^6 * (7 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 6 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))))) + (269325 * (5 * alpha^4) * (1 - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
25 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 10 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha)) + 269325 * alpha^5 * (25 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 10 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))))) + (63273 * (4 *
alpha^3) * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 63273 * alpha^4 * (31 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 90 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + 65 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 15 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))))) + (9450 * (3 * alpha^2) * (1 - 63 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) +
301 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) - 350 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) +
140 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) - 21 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha)) + 9450 * alpha^3 * (301 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 63 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 350 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + 140 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) - 21 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) + (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))))) + (870 * (2 * alpha) *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 870 * alpha^2 * (127 *
(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 966 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + 1701 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 1050 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) + 266 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) - 28 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(7/alpha^2))))) + (45 * (1 - 255 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 45 * alpha *
(3025 * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(2/alpha^2))) - 255 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) - 1) *
((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (1/alpha^2))) - 7770 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) + 6951 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) *
((4/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) - 2646 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) + 462 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) *
((6/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))) - 36 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) +
(-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) +
(-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(7/alpha^2))) + (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) - 1) *
((8/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (8/alpha^2))))) + 511 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((1/alpha) -
1) * ((1/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2))) - 9330 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((2/alpha) - 1) * ((2/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (2/alpha^2))) + 34105 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((3/alpha) -
1) * ((3/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(3/alpha^2))) - 42525 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((4/alpha) - 1) * ((4/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (4/alpha^2))) + 22827 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((5/alpha) -
1) * ((5/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(5/alpha^2))) - 5880 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((6/alpha) - 1) * ((6/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (6/alpha^2))) + 750 * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((7/alpha) -
1) * ((7/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(7/alpha^2))) - 45 * (((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^((8/alpha) - 1) * ((8/alpha) *
((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) +
(-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) +
(-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) +
(-log(u9))^alpha * log((-log(u9))))) - ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha) *
(log(((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)) * (8/alpha^2))) + (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((9/alpha) -
1) * ((9/alpha) * ((-log(u1))^alpha * log((-log(u1))) + (-log(u10))^alpha *
log((-log(u10))) + (-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) + (-log(u5))^alpha *
log((-log(u5))) + (-log(u6))^alpha * log((-log(u6))) + (-log(u7))^alpha *
log((-log(u7))) + (-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(9/alpha^2))))) * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(-10 + 1/alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 + 1026576 *
alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * (((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^((-10 +
1/alpha) - 1) * ((-10 + 1/alpha) * ((-log(u1))^alpha * log((-log(u1))) +
(-log(u10))^alpha * log((-log(u10))) + (-log(u2))^alpha *
log((-log(u2))) + (-log(u3))^alpha * log((-log(u3))) + (-log(u4))^alpha *
log((-log(u4))) + (-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) + (-log(u8))^alpha *
log((-log(u8))) + (-log(u9))^alpha * log((-log(u9))))) -
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(-10 + 1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) * (-log(u9))^(-1 + alpha) + (-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 + 1026576 *
alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * ((-log(u9))^(-1 + alpha) * log((-log(u9)))))/(E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
u1 * u10 * u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9) - ((-log(u1))^(-1 +
alpha) * (-log(u10))^(-1 + alpha) * (-log(u2))^(-1 + alpha) *
(-log(u3))^(-1 + alpha) * (-log(u4))^(-1 + alpha) * (-log(u5))^(-1 +
alpha) * (-log(u6))^(-1 + alpha) * (-log(u7))^(-1 + alpha) *
(-log(u8))^(-1 + alpha) * (-1 + 362880 * alpha^9 + 1026576 *
alpha^8 * (-1 + ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha)) + 1172700 * alpha^7 * (1 - 3 *
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha)) + 723680 *
alpha^6 * (-1 + 7 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 6 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha)) + 269325 * alpha^5 * (1 -
15 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 25 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
10 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha)) + 63273 *
alpha^4 * (-1 + 31 * ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) - 90 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
65 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 15 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha)) + 9450 * alpha^3 * (1 -
63 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 301 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
350 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 140 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
21 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha)) + 870 * alpha^2 *
(-1 + 127 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) - 966 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) +
1701 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) - 1050 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) +
266 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) - 28 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) +
((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha)) + 45 * alpha * (1 -
255 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(1/alpha) + 3025 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(2/alpha) -
7770 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(3/alpha) + 6951 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(4/alpha) -
2646 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(5/alpha) + 462 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(6/alpha) -
36 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(7/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(8/alpha)) + 511 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) -
9330 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(2/alpha) + 34105 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(3/alpha) -
42525 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(4/alpha) + 22827 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(5/alpha) -
5880 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(6/alpha) + 750 * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(7/alpha) -
45 * ((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^(8/alpha) + ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(9/alpha)) * ((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(-10 +
1/alpha) * (-log(u9))^(-1 + alpha)) * (E^((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) *
(log(E) * (((-log(u1))^alpha + (-log(u10))^alpha + (-log(u2))^alpha +
(-log(u3))^alpha + (-log(u4))^alpha + (-log(u5))^alpha +
(-log(u6))^alpha + (-log(u7))^alpha + (-log(u8))^alpha +
(-log(u9))^alpha)^((1/alpha) - 1) * ((1/alpha) * ((-log(u1))^alpha *
log((-log(u1))) + (-log(u10))^alpha * log((-log(u10))) +
(-log(u2))^alpha * log((-log(u2))) + (-log(u3))^alpha *
log((-log(u3))) + (-log(u4))^alpha * log((-log(u4))) +
(-log(u5))^alpha * log((-log(u5))) + (-log(u6))^alpha *
log((-log(u6))) + (-log(u7))^alpha * log((-log(u7))) +
(-log(u8))^alpha * log((-log(u8))) + (-log(u9))^alpha *
log((-log(u9))))) - ((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * (log(((-log(u1))^alpha +
(-log(u10))^alpha + (-log(u2))^alpha + (-log(u3))^alpha +
(-log(u4))^alpha + (-log(u5))^alpha + (-log(u6))^alpha +
(-log(u7))^alpha + (-log(u8))^alpha + (-log(u9))^alpha)) *
(1/alpha^2)))) * u1 * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9)/(E^((-log(u1))^alpha + (-log(u10))^alpha +
(-log(u2))^alpha + (-log(u3))^alpha + (-log(u4))^alpha +
(-log(u5))^alpha + (-log(u6))^alpha + (-log(u7))^alpha +
(-log(u8))^alpha + (-log(u9))^alpha)^(1/alpha) * u1 * u10 *
u2 * u3 * u4 * u5 * u6 * u7 * u8 * u9)^2)
`gumbelCopula.pdfDerWrtPar.algr` <-
expression({
.expr1 <- log(u1)
.expr2 <- -.expr1
.expr3 <- .expr2^alpha
.expr4 <- 1/alpha
.expr11 <- .expr3^.expr4
.expr17 <- .expr3^(.expr4 - 1) * (.expr4 * (.expr3 * log(.expr2))) -
.expr11 * (log(.expr3) * (1/alpha^2))
.expr18 <- E^.expr11
.expr20 <- .expr18 * u1 * .expr1
.value <- -(.expr17/.expr20 - .expr11 * (.expr18 * (log(E) *
.expr17) * u1 * .expr1)/.expr20^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr4 <- -1 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr8 <- .expr2^alpha
.expr10 <- -log(u2)
.expr11 <- .expr10^alpha
.expr12 <- .expr8 + .expr11
.expr13 <- 1/alpha
.expr14 <- .expr12^.expr13
.expr15 <- .expr4 + .expr14
.expr20 <- log(.expr10)
.expr22 <- .expr8 * .expr6 + .expr11 * .expr20
.expr28 <- log(.expr12) * (1/alpha^2)
.expr30 <- .expr12^(.expr13 - 1) * (.expr13 * .expr22) -
.expr14 * .expr28
.expr35 <- -2 + .expr13
.expr36 <- .expr12^.expr35
.expr38 <- .expr5 * .expr15
.expr47 <- .expr10^.expr4
.expr49 <- .expr38 * .expr36
.expr53 <- E^.expr14
.expr55 <- .expr53 * u1 * u2
.value <- (((.expr5 * .expr6 * .expr15 + .expr5 * (1 + .expr30)) *
.expr36 + .expr38 * (.expr12^(.expr35 - 1) * (.expr35 *
.expr22) - .expr36 * .expr28)) * .expr47 + .expr49 *
(.expr47 * .expr20))/.expr55 - .expr49 * .expr47 * (.expr53 *
(log(E) * .expr30) * u1 * u2)/.expr55^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr16 <- alpha^2
.expr19 <- 3 * alpha
.expr20 <- .expr2^alpha
.expr21 <- .expr9^alpha
.expr24 <- -log(u3)
.expr25 <- .expr24^alpha
.expr26 <- .expr20 + .expr21 + .expr25
.expr27 <- 1/alpha
.expr28 <- .expr26^.expr27
.expr29 <- .expr3 + .expr28
.expr34 <- 2/alpha
.expr35 <- .expr26^.expr34
.expr36 <- 1 + 2 * .expr16 + .expr19 * .expr29 - 3 * .expr28 +
.expr35
.expr38 <- .expr5 * .expr10
.expr47 <- log(.expr24)
.expr49 <- .expr20 * .expr6 + .expr21 * .expr12 + .expr25 *
.expr47
.expr52 <- log(.expr26)
.expr54 <- .expr52 * (1/.expr16)
.expr56 <- .expr26^(.expr27 - 1) * (.expr27 * .expr49) -
.expr28 * .expr54
.expr74 <- -3 + .expr27
.expr75 <- .expr26^.expr74
.expr77 <- .expr38 * .expr36
.expr86 <- .expr24^.expr4
.expr88 <- .expr77 * .expr75
.expr92 <- E^.expr28
.expr95 <- .expr92 * u1 * u2 * u3
.value <- ((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr36 + .expr38 * (2 * (2 * alpha) + (3 *
.expr29 + .expr19 * .expr56) - 3 * .expr56 + (.expr26^(.expr34 -
1) * (.expr34 * .expr49) - .expr35 * (.expr52 * (2/.expr16))))) *
.expr75 + .expr77 * (.expr26^(.expr74 - 1) * (.expr74 *
.expr49) - .expr75 * .expr54)) * .expr86 + .expr88 *
(.expr86 * .expr47))/.expr95 - .expr88 * .expr86 * (.expr92 *
(log(E) * .expr56) * u1 * u2 * u3)/.expr95^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr28 <- alpha^2
.expr29 <- 11 * .expr28
.expr30 <- .expr2^alpha
.expr31 <- .expr9^alpha
.expr33 <- .expr17^alpha
.expr36 <- -log(u4)
.expr37 <- .expr36^alpha
.expr38 <- .expr30 + .expr31 + .expr33 + .expr37
.expr39 <- 1/alpha
.expr40 <- .expr38^.expr39
.expr41 <- .expr3 + .expr40
.expr44 <- 6 * alpha
.expr47 <- 2/alpha
.expr48 <- .expr38^.expr47
.expr49 <- 1 - 3 * .expr40 + .expr48
.expr56 <- 3/alpha
.expr57 <- .expr38^.expr56
.expr58 <- .expr3 + 6 * alpha^3 + .expr29 * .expr41 + .expr44 *
.expr49 + 7 * .expr40 - 6 * .expr48 + .expr57
.expr60 <- .expr20 * .expr18
.expr73 <- log(.expr36)
.expr75 <- .expr30 * .expr6 + .expr31 * .expr12 + .expr33 *
.expr21 + .expr37 * .expr73
.expr78 <- log(.expr38)
.expr80 <- .expr78 * (1/.expr28)
.expr82 <- .expr38^(.expr39 - 1) * (.expr39 * .expr75) -
.expr40 * .expr80
.expr94 <- .expr38^(.expr47 - 1) * (.expr47 * .expr75) -
.expr48 * (.expr78 * (2/.expr28))
.expr116 <- -4 + .expr39
.expr117 <- .expr38^.expr116
.expr119 <- .expr60 * .expr58
.expr128 <- .expr36^.expr4
.expr130 <- .expr119 * .expr117
.expr134 <- E^.expr40
.expr138 <- .expr134 * u1 * u2 * u3 * u4
.value <- (((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr58 + .expr60 * (6 * (3 * .expr28) + (11 * (2 * alpha) *
.expr41 + .expr29 * .expr82) + (6 * .expr49 + .expr44 *
(.expr94 - 3 * .expr82)) + 7 * .expr82 - 6 * .expr94 +
(.expr38^(.expr56 - 1) * (.expr56 * .expr75) - .expr57 *
(.expr78 * (3/.expr28))))) * .expr117 + .expr119 *
(.expr38^(.expr116 - 1) * (.expr116 * .expr75) - .expr117 *
.expr80)) * .expr128 + .expr130 * (.expr128 * .expr73))/.expr138 -
.expr130 * .expr128 * (.expr134 * (log(E) * .expr82) *
u1 * u2 * u3 * u4)/.expr138^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr37 <- alpha^3
.expr38 <- 50 * .expr37
.expr39 <- .expr2^alpha
.expr40 <- .expr9^alpha
.expr42 <- .expr17^alpha
.expr44 <- .expr26^alpha
.expr47 <- -log(u5)
.expr48 <- .expr47^alpha
.expr49 <- .expr39 + .expr40 + .expr42 + .expr44 + .expr48
.expr50 <- 1/alpha
.expr51 <- .expr49^.expr50
.expr52 <- .expr3 + .expr51
.expr55 <- alpha^2
.expr56 <- 35 * .expr55
.expr59 <- 2/alpha
.expr60 <- .expr49^.expr59
.expr61 <- 1 - 3 * .expr51 + .expr60
.expr64 <- 10 * alpha
.expr69 <- 3/alpha
.expr70 <- .expr49^.expr69
.expr71 <- .expr3 + 7 * .expr51 - 6 * .expr60 + .expr70
.expr80 <- 4/alpha
.expr81 <- .expr49^.expr80
.expr82 <- .expr3 - 24 * alpha^4 - .expr38 * .expr52 - .expr56 *
.expr61 - .expr64 * .expr71 + 15 * .expr51 - 25 * .expr60 +
10 * .expr70 - .expr81
.expr84 <- .expr29 * .expr27
.expr94 <- log(.expr47)
.expr96 <- .expr39 * .expr6 + .expr40 * .expr12 + .expr42 *
.expr21 + .expr44 * .expr30 + .expr48 * .expr94
.expr99 <- log(.expr49)
.expr101 <- .expr99 * (1/.expr55)
.expr103 <- .expr49^(.expr50 - 1) * (.expr50 * .expr96) -
.expr51 * .expr101
.expr123 <- .expr49^(.expr59 - 1) * (.expr59 * .expr96) -
.expr60 * (.expr99 * (2/.expr55))
.expr140 <- .expr49^(.expr69 - 1) * (.expr69 * .expr96) -
.expr70 * (.expr99 * (3/.expr55))
.expr162 <- -5 + .expr50
.expr163 <- .expr49^.expr162
.expr165 <- .expr84 * .expr82
.expr174 <- .expr47^.expr4
.expr176 <- .expr165 * .expr163
.expr180 <- E^.expr51
.expr185 <- .expr180 * u1 * u2 * u3 * u4 * u5
.value <- -(((((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr27 + .expr29 * (.expr27 * .expr30)) * .expr82 +
.expr84 * (15 * .expr103 - (24 * (4 * .expr37) + (50 *
(3 * .expr55) * .expr52 + .expr38 * .expr103) + (35 *
(2 * alpha) * .expr61 + .expr56 * (.expr123 - 3 *
.expr103)) + (10 * .expr71 + .expr64 * (7 * .expr103 -
6 * .expr123 + .expr140))) - 25 * .expr123 + 10 *
.expr140 - (.expr49^(.expr80 - 1) * (.expr80 * .expr96) -
.expr81 * (.expr99 * (4/.expr55))))) * .expr163 +
.expr165 * (.expr49^(.expr162 - 1) * (.expr162 * .expr96) -
.expr163 * .expr101)) * .expr174 + .expr176 * (.expr174 *
.expr94))/.expr185 - .expr176 * .expr174 * (.expr180 *
(log(E) * .expr103) * u1 * u2 * u3 * u4 * u5)/.expr185^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr46 <- alpha^4
.expr47 <- 274 * .expr46
.expr48 <- .expr2^alpha
.expr49 <- .expr9^alpha
.expr51 <- .expr17^alpha
.expr53 <- .expr26^alpha
.expr55 <- .expr35^alpha
.expr58 <- -log(u6)
.expr59 <- .expr58^alpha
.expr60 <- .expr48 + .expr49 + .expr51 + .expr53 + .expr55 +
.expr59
.expr61 <- 1/alpha
.expr62 <- .expr60^.expr61
.expr63 <- .expr3 + .expr62
.expr66 <- alpha^3
.expr67 <- 225 * .expr66
.expr70 <- 2/alpha
.expr71 <- .expr60^.expr70
.expr72 <- 1 - 3 * .expr62 + .expr71
.expr75 <- alpha^2
.expr76 <- 85 * .expr75
.expr81 <- 3/alpha
.expr82 <- .expr60^.expr81
.expr83 <- .expr3 + 7 * .expr62 - 6 * .expr71 + .expr82
.expr86 <- 15 * alpha
.expr93 <- 4/alpha
.expr94 <- .expr60^.expr93
.expr95 <- 1 - 15 * .expr62 + 25 * .expr71 - 10 * .expr82 +
.expr94
.expr106 <- 5/alpha
.expr107 <- .expr60^.expr106
.expr108 <- .expr3 + 120 * alpha^5 + .expr47 * .expr63 +
.expr67 * .expr72 + .expr76 * .expr83 + .expr86 * .expr95 +
31 * .expr62 - 90 * .expr71 + 65 * .expr82 - 15 * .expr94 +
.expr107
.expr110 <- .expr38 * .expr36
.expr127 <- log(.expr58)
.expr129 <- .expr48 * .expr6 + .expr49 * .expr12 + .expr51 *
.expr21 + .expr53 * .expr30 + .expr55 * .expr39 + .expr59 *
.expr127
.expr132 <- log(.expr60)
.expr134 <- .expr132 * (1/.expr75)
.expr136 <- .expr60^(.expr61 - 1) * (.expr61 * .expr129) -
.expr62 * .expr134
.expr150 <- .expr60^(.expr70 - 1) * (.expr70 * .expr129) -
.expr71 * (.expr132 * (2/.expr75))
.expr169 <- .expr60^(.expr81 - 1) * (.expr81 * .expr129) -
.expr82 * (.expr132 * (3/.expr75))
.expr187 <- .expr60^(.expr93 - 1) * (.expr93 * .expr129) -
.expr94 * (.expr132 * (4/.expr75))
.expr212 <- -6 + .expr61
.expr213 <- .expr60^.expr212
.expr215 <- .expr110 * .expr108
.expr224 <- .expr58^.expr4
.expr226 <- .expr215 * .expr213
.expr230 <- E^.expr62
.expr236 <- .expr230 * u1 * u2 * u3 * u4 * u5 * u6
.value <- (((((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr27 + .expr29 * (.expr27 * .expr30)) * .expr36 +
.expr38 * (.expr36 * .expr39)) * .expr108 + .expr110 *
(120 * (5 * .expr46) + (274 * (4 * .expr66) * .expr63 +
.expr47 * .expr136) + (225 * (3 * .expr75) * .expr72 +
.expr67 * (.expr150 - 3 * .expr136)) + (85 * (2 *
alpha) * .expr83 + .expr76 * (7 * .expr136 - 6 *
.expr150 + .expr169)) + (15 * .expr95 + .expr86 *
(25 * .expr150 - 15 * .expr136 - 10 * .expr169 +
.expr187)) + 31 * .expr136 - 90 * .expr150 +
65 * .expr169 - 15 * .expr187 + (.expr60^(.expr106 -
1) * (.expr106 * .expr129) - .expr107 * (.expr132 *
(5/.expr75))))) * .expr213 + .expr215 * (.expr60^(.expr212 -
1) * (.expr212 * .expr129) - .expr213 * .expr134)) *
.expr224 + .expr226 * (.expr224 * .expr127))/.expr236 -
.expr226 * .expr224 * (.expr230 * (log(E) * .expr136) *
u1 * u2 * u3 * u4 * u5 * u6)/.expr236^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u6)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr55 <- alpha^5
.expr56 <- 1764 * .expr55
.expr57 <- .expr2^alpha
.expr58 <- .expr9^alpha
.expr60 <- .expr17^alpha
.expr62 <- .expr26^alpha
.expr64 <- .expr35^alpha
.expr66 <- .expr44^alpha
.expr69 <- -log(u7)
.expr70 <- .expr69^alpha
.expr71 <- .expr57 + .expr58 + .expr60 + .expr62 + .expr64 +
.expr66 + .expr70
.expr72 <- 1/alpha
.expr73 <- .expr71^.expr72
.expr74 <- .expr3 + .expr73
.expr77 <- alpha^4
.expr78 <- 1624 * .expr77
.expr81 <- 2/alpha
.expr82 <- .expr71^.expr81
.expr83 <- 1 - 3 * .expr73 + .expr82
.expr86 <- alpha^3
.expr87 <- 735 * .expr86
.expr92 <- 3/alpha
.expr93 <- .expr71^.expr92
.expr94 <- .expr3 + 7 * .expr73 - 6 * .expr82 + .expr93
.expr97 <- alpha^2
.expr98 <- 175 * .expr97
.expr105 <- 4/alpha
.expr106 <- .expr71^.expr105
.expr107 <- 1 - 15 * .expr73 + 25 * .expr82 - 10 * .expr93 +
.expr106
.expr110 <- 21 * alpha
.expr119 <- 5/alpha
.expr120 <- .expr71^.expr119
.expr121 <- .expr3 + 31 * .expr73 - 90 * .expr82 + 65 * .expr93 -
15 * .expr106 + .expr120
.expr134 <- 6/alpha
.expr135 <- .expr71^.expr134
.expr136 <- .expr3 - 720 * alpha^6 - .expr56 * .expr74 -
.expr78 * .expr83 - .expr87 * .expr94 - .expr98 * .expr107 -
.expr110 * .expr121 + 63 * .expr73 - 301 * .expr82 +
350 * .expr93 - 140 * .expr106 + 21 * .expr120 - .expr135
.expr138 <- .expr47 * .expr45
.expr152 <- log(.expr69)
.expr154 <- .expr57 * .expr6 + .expr58 * .expr12 + .expr60 *
.expr21 + .expr62 * .expr30 + .expr64 * .expr39 + .expr66 *
.expr48 + .expr70 * .expr152
.expr157 <- log(.expr71)
.expr159 <- .expr157 * (1/.expr97)
.expr161 <- .expr71^(.expr72 - 1) * (.expr72 * .expr154) -
.expr73 * .expr159
.expr181 <- .expr71^(.expr81 - 1) * (.expr81 * .expr154) -
.expr82 * (.expr157 * (2/.expr97))
.expr200 <- .expr71^(.expr92 - 1) * (.expr92 * .expr154) -
.expr93 * (.expr157 * (3/.expr97))
.expr220 <- .expr71^(.expr105 - 1) * (.expr105 * .expr154) -
.expr106 * (.expr157 * (4/.expr97))
.expr240 <- .expr71^(.expr119 - 1) * (.expr119 * .expr154) -
.expr120 * (.expr157 * (5/.expr97))
.expr266 <- -7 + .expr72
.expr267 <- .expr71^.expr266
.expr269 <- .expr138 * .expr136
.expr278 <- .expr69^.expr4
.expr280 <- .expr269 * .expr267
.expr284 <- E^.expr73
.expr291 <- .expr284 * u1 * u2 * u3 * u4 * u5 * u6 * u7
.value <- -(((((((((.expr5 * .expr6 * .expr10 + .expr5 *
(.expr10 * .expr12)) * .expr18 + .expr20 * (.expr18 *
.expr21)) * .expr27 + .expr29 * (.expr27 * .expr30)) *
.expr36 + .expr38 * (.expr36 * .expr39)) * .expr45 +
.expr47 * (.expr45 * .expr48)) * .expr136 + .expr138 *
(63 * .expr161 - (720 * (6 * .expr55) + (1764 * (5 *
.expr77) * .expr74 + .expr56 * .expr161) + (1624 *
(4 * .expr86) * .expr83 + .expr78 * (.expr181 - 3 *
.expr161)) + (735 * (3 * .expr97) * .expr94 + .expr87 *
(7 * .expr161 - 6 * .expr181 + .expr200)) + (175 *
(2 * alpha) * .expr107 + .expr98 * (25 * .expr181 -
15 * .expr161 - 10 * .expr200 + .expr220)) + (21 *
.expr121 + .expr110 * (31 * .expr161 - 90 * .expr181 +
65 * .expr200 - 15 * .expr220 + .expr240))) - 301 *
.expr181 + 350 * .expr200 - 140 * .expr220 + 21 *
.expr240 - (.expr71^(.expr134 - 1) * (.expr134 *
.expr154) - .expr135 * (.expr157 * (6/.expr97))))) *
.expr267 + .expr269 * (.expr71^(.expr266 - 1) * (.expr266 *
.expr154) - .expr267 * .expr159)) * .expr278 + .expr280 *
(.expr278 * .expr152))/.expr291 - .expr280 * .expr278 *
(.expr284 * (log(E) * .expr161) * u1 * u2 * u3 * u4 *
u5 * u6 * u7)/.expr291^2)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u6)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr53 <- -log(u7)
.expr54 <- .expr53^.expr4
.expr56 <- .expr47 * .expr45
.expr57 <- log(.expr53)
.expr64 <- alpha^6
.expr65 <- 13068 * .expr64
.expr66 <- .expr2^alpha
.expr67 <- .expr9^alpha
.expr69 <- .expr17^alpha
.expr71 <- .expr26^alpha
.expr73 <- .expr35^alpha
.expr75 <- .expr44^alpha
.expr77 <- .expr53^alpha
.expr80 <- -log(u8)
.expr81 <- .expr80^alpha
.expr82 <- .expr66 + .expr67 + .expr69 + .expr71 + .expr73 +
.expr75 + .expr77 + .expr81
.expr83 <- 1/alpha
.expr84 <- .expr82^.expr83
.expr85 <- .expr3 + .expr84
.expr88 <- alpha^5
.expr89 <- 13132 * .expr88
.expr92 <- 2/alpha
.expr93 <- .expr82^.expr92
.expr94 <- 1 - 3 * .expr84 + .expr93
.expr97 <- alpha^4
.expr98 <- 6769 * .expr97
.expr103 <- 3/alpha
.expr104 <- .expr82^.expr103
.expr105 <- .expr3 + 7 * .expr84 - 6 * .expr93 + .expr104
.expr108 <- alpha^3
.expr109 <- 1960 * .expr108
.expr116 <- 4/alpha
.expr117 <- .expr82^.expr116
.expr118 <- 1 - 15 * .expr84 + 25 * .expr93 - 10 * .expr104 +
.expr117
.expr121 <- alpha^2
.expr122 <- 322 * .expr121
.expr131 <- 5/alpha
.expr132 <- .expr82^.expr131
.expr133 <- .expr3 + 31 * .expr84 - 90 * .expr93 + 65 * .expr104 -
15 * .expr117 + .expr132
.expr136 <- 28 * alpha
.expr147 <- 6/alpha
.expr148 <- .expr82^.expr147
.expr149 <- 1 - 63 * .expr84 + 301 * .expr93 - 350 * .expr104 +
140 * .expr117 - 21 * .expr132 + .expr148
.expr164 <- 7/alpha
.expr165 <- .expr82^.expr164
.expr166 <- .expr3 + 5040 * alpha^7 + .expr65 * .expr85 +
.expr89 * .expr94 + .expr98 * .expr105 + .expr109 * .expr118 +
.expr122 * .expr133 + .expr136 * .expr149 + 127 * .expr84 -
966 * .expr93 + 1701 * .expr104 - 1050 * .expr117 + 266 *
.expr132 - 28 * .expr148 + .expr165
.expr168 <- .expr56 * .expr54
.expr189 <- log(.expr80)
.expr191 <- .expr66 * .expr6 + .expr67 * .expr12 + .expr69 *
.expr21 + .expr71 * .expr30 + .expr73 * .expr39 + .expr75 *
.expr48 + .expr77 * .expr57 + .expr81 * .expr189
.expr194 <- log(.expr82)
.expr196 <- .expr194 * (1/.expr121)
.expr198 <- .expr82^(.expr83 - 1) * (.expr83 * .expr191) -
.expr84 * .expr196
.expr212 <- .expr82^(.expr92 - 1) * (.expr92 * .expr191) -
.expr93 * (.expr194 * (2/.expr121))
.expr231 <- .expr82^(.expr103 - 1) * (.expr103 * .expr191) -
.expr104 * (.expr194 * (3/.expr121))
.expr251 <- .expr82^(.expr116 - 1) * (.expr116 * .expr191) -
.expr117 * (.expr194 * (4/.expr121))
.expr273 <- .expr82^(.expr131 - 1) * (.expr131 * .expr191) -
.expr132 * (.expr194 * (5/.expr121))
.expr295 <- .expr82^(.expr147 - 1) * (.expr147 * .expr191) -
.expr148 * (.expr194 * (6/.expr121))
.expr324 <- -8 + .expr83
.expr325 <- .expr82^.expr324
.expr327 <- .expr168 * .expr166
.expr336 <- .expr80^.expr4
.expr338 <- .expr327 * .expr325
.expr342 <- E^.expr84
.expr350 <- .expr342 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8
.value <- (((((((((.expr5 * .expr6 * .expr10 + .expr5 * (.expr10 *
.expr12)) * .expr18 + .expr20 * (.expr18 * .expr21)) *
.expr27 + .expr29 * (.expr27 * .expr30)) * .expr36 +
.expr38 * (.expr36 * .expr39)) * .expr45 + .expr47 *
(.expr45 * .expr48)) * .expr54 + .expr56 * (.expr54 *
.expr57)) * .expr166 + .expr168 * (5040 * (7 * .expr64) +
(13068 * (6 * .expr88) * .expr85 + .expr65 * .expr198) +
(13132 * (5 * .expr97) * .expr94 + .expr89 * (.expr212 -
3 * .expr198)) + (6769 * (4 * .expr108) * .expr105 +
.expr98 * (7 * .expr198 - 6 * .expr212 + .expr231)) +
(1960 * (3 * .expr121) * .expr118 + .expr109 * (25 *
.expr212 - 15 * .expr198 - 10 * .expr231 + .expr251)) +
(322 * (2 * alpha) * .expr133 + .expr122 * (31 * .expr198 -
90 * .expr212 + 65 * .expr231 - 15 * .expr251 + .expr273)) +
(28 * .expr149 + .expr136 * (301 * .expr212 - 63 * .expr198 -
350 * .expr231 + 140 * .expr251 - 21 * .expr273 +
.expr295)) + 127 * .expr198 - 966 * .expr212 + 1701 *
.expr231 - 1050 * .expr251 + 266 * .expr273 - 28 * .expr295 +
(.expr82^(.expr164 - 1) * (.expr164 * .expr191) - .expr165 *
(.expr194 * (7/.expr121))))) * .expr325 + .expr327 *
(.expr82^(.expr324 - 1) * (.expr324 * .expr191) - .expr325 *
.expr196)) * .expr336 + .expr338 * (.expr336 * .expr189))/.expr350 -
.expr338 * .expr336 * (.expr342 * (log(E) * .expr198) *
u1 * u2 * u3 * u4 * u5 * u6 * u7 * u8)/.expr350^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u2)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u3)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u4)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u5)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u6)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr53 <- -log(u7)
.expr54 <- .expr53^.expr4
.expr56 <- .expr47 * .expr45
.expr57 <- log(.expr53)
.expr62 <- -log(u8)
.expr63 <- .expr62^.expr4
.expr65 <- .expr56 * .expr54
.expr66 <- log(.expr62)
.expr73 <- alpha^7
.expr74 <- 109584 * .expr73
.expr75 <- .expr2^alpha
.expr76 <- .expr9^alpha
.expr78 <- .expr17^alpha
.expr80 <- .expr26^alpha
.expr82 <- .expr35^alpha
.expr84 <- .expr44^alpha
.expr86 <- .expr53^alpha
.expr88 <- .expr62^alpha
.expr91 <- -log(u9)
.expr92 <- .expr91^alpha
.expr93 <- .expr75 + .expr76 + .expr78 + .expr80 + .expr82 +
.expr84 + .expr86 + .expr88 + .expr92
.expr94 <- 1/alpha
.expr95 <- .expr93^.expr94
.expr96 <- .expr3 + .expr95
.expr99 <- alpha^6
.expr100 <- 118124 * .expr99
.expr103 <- 2/alpha
.expr104 <- .expr93^.expr103
.expr105 <- 1 - 3 * .expr95 + .expr104
.expr108 <- alpha^5
.expr109 <- 67284 * .expr108
.expr114 <- 3/alpha
.expr115 <- .expr93^.expr114
.expr116 <- .expr3 + 7 * .expr95 - 6 * .expr104 + .expr115
.expr119 <- alpha^4
.expr120 <- 22449 * .expr119
.expr127 <- 4/alpha
.expr128 <- .expr93^.expr127
.expr129 <- 1 - 15 * .expr95 + 25 * .expr104 - 10 * .expr115 +
.expr128
.expr132 <- alpha^3
.expr133 <- 4536 * .expr132
.expr142 <- 5/alpha
.expr143 <- .expr93^.expr142
.expr144 <- .expr3 + 31 * .expr95 - 90 * .expr104 + 65 *
.expr115 - 15 * .expr128 + .expr143
.expr147 <- alpha^2
.expr148 <- 546 * .expr147
.expr159 <- 6/alpha
.expr160 <- .expr93^.expr159
.expr161 <- 1 - 63 * .expr95 + 301 * .expr104 - 350 * .expr115 +
140 * .expr128 - 21 * .expr143 + .expr160
.expr164 <- 36 * alpha
.expr177 <- 7/alpha
.expr178 <- .expr93^.expr177
.expr179 <- .expr3 + 127 * .expr95 - 966 * .expr104 + 1701 *
.expr115 - 1050 * .expr128 + 266 * .expr143 - 28 * .expr160 +
.expr178
.expr196 <- 8/alpha
.expr197 <- .expr93^.expr196
.expr198 <- 1 + 40320 * alpha^8 + .expr74 * .expr96 + .expr100 *
.expr105 + .expr109 * .expr116 + .expr120 * .expr129 +
.expr133 * .expr144 + .expr148 * .expr161 + .expr164 *
.expr179 - 255 * .expr95 + 3025 * .expr104 - 7770 * .expr115 +
6951 * .expr128 - 2646 * .expr143 + 462 * .expr160 -
36 * .expr178 + .expr197
.expr200 <- .expr65 * .expr63
.expr223 <- log(.expr91)
.expr225 <- .expr75 * .expr6 + .expr76 * .expr12 + .expr78 *
.expr21 + .expr80 * .expr30 + .expr82 * .expr39 + .expr84 *
.expr48 + .expr86 * .expr57 + .expr88 * .expr66 + .expr92 *
.expr223
.expr228 <- log(.expr93)
.expr230 <- .expr228 * (1/.expr147)
.expr232 <- .expr93^(.expr94 - 1) * (.expr94 * .expr225) -
.expr95 * .expr230
.expr246 <- .expr93^(.expr103 - 1) * (.expr103 * .expr225) -
.expr104 * (.expr228 * (2/.expr147))
.expr265 <- .expr93^(.expr114 - 1) * (.expr114 * .expr225) -
.expr115 * (.expr228 * (3/.expr147))
.expr285 <- .expr93^(.expr127 - 1) * (.expr127 * .expr225) -
.expr128 * (.expr228 * (4/.expr147))
.expr307 <- .expr93^(.expr142 - 1) * (.expr142 * .expr225) -
.expr143 * (.expr228 * (5/.expr147))
.expr331 <- .expr93^(.expr159 - 1) * (.expr159 * .expr225) -
.expr160 * (.expr228 * (6/.expr147))
.expr355 <- .expr93^(.expr177 - 1) * (.expr177 * .expr225) -
.expr178 * (.expr228 * (7/.expr147))
.expr386 <- -9 + .expr94
.expr387 <- .expr93^.expr386
.expr389 <- .expr200 * .expr198
.expr398 <- .expr91^.expr4
.expr400 <- .expr389 * .expr387
.expr404 <- E^.expr95
.expr413 <- .expr404 * u1 * u2 * u3 * u4 * u5 * u6 * u7 *
u8 * u9
.value <- ((((((((((.expr5 * .expr6 * .expr10 + .expr5 *
(.expr10 * .expr12)) * .expr18 + .expr20 * (.expr18 *
.expr21)) * .expr27 + .expr29 * (.expr27 * .expr30)) *
.expr36 + .expr38 * (.expr36 * .expr39)) * .expr45 +
.expr47 * (.expr45 * .expr48)) * .expr54 + .expr56 *
(.expr54 * .expr57)) * .expr63 + .expr65 * (.expr63 *
.expr66)) * .expr198 + .expr200 * (40320 * (8 * .expr73) +
(109584 * (7 * .expr99) * .expr96 + .expr74 * .expr232) +
(118124 * (6 * .expr108) * .expr105 + .expr100 * (.expr246 -
3 * .expr232)) + (67284 * (5 * .expr119) * .expr116 +
.expr109 * (7 * .expr232 - 6 * .expr246 + .expr265)) +
(22449 * (4 * .expr132) * .expr129 + .expr120 * (25 *
.expr246 - 15 * .expr232 - 10 * .expr265 + .expr285)) +
(4536 * (3 * .expr147) * .expr144 + .expr133 * (31 *
.expr232 - 90 * .expr246 + 65 * .expr265 - 15 * .expr285 +
.expr307)) + (546 * (2 * alpha) * .expr161 + .expr148 *
(301 * .expr246 - 63 * .expr232 - 350 * .expr265 + 140 *
.expr285 - 21 * .expr307 + .expr331)) + (36 * .expr179 +
.expr164 * (127 * .expr232 - 966 * .expr246 + 1701 *
.expr265 - 1050 * .expr285 + 266 * .expr307 - 28 *
.expr331 + .expr355)) - 255 * .expr232 + 3025 * .expr246 -
7770 * .expr265 + 6951 * .expr285 - 2646 * .expr307 +
462 * .expr331 - 36 * .expr355 + (.expr93^(.expr196 -
1) * (.expr196 * .expr225) - .expr197 * (.expr228 * (8/.expr147))))) *
.expr387 + .expr389 * (.expr93^(.expr386 - 1) * (.expr386 *
.expr225) - .expr387 * .expr230)) * .expr398 + .expr400 *
(.expr398 * .expr223))/.expr413 - .expr400 * .expr398 *
(.expr404 * (log(E) * .expr232) * u1 * u2 * u3 * u4 *
u5 * u6 * u7 * u8 * u9)/.expr413^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr2 <- -log(u1)
.expr3 <- -1
.expr4 <- .expr3 + alpha
.expr5 <- .expr2^.expr4
.expr6 <- log(.expr2)
.expr9 <- -log(u10)
.expr10 <- .expr9^.expr4
.expr12 <- log(.expr9)
.expr17 <- -log(u2)
.expr18 <- .expr17^.expr4
.expr20 <- .expr5 * .expr10
.expr21 <- log(.expr17)
.expr26 <- -log(u3)
.expr27 <- .expr26^.expr4
.expr29 <- .expr20 * .expr18
.expr30 <- log(.expr26)
.expr35 <- -log(u4)
.expr36 <- .expr35^.expr4
.expr38 <- .expr29 * .expr27
.expr39 <- log(.expr35)
.expr44 <- -log(u5)
.expr45 <- .expr44^.expr4
.expr47 <- .expr38 * .expr36
.expr48 <- log(.expr44)
.expr53 <- -log(u6)
.expr54 <- .expr53^.expr4
.expr56 <- .expr47 * .expr45
.expr57 <- log(.expr53)
.expr62 <- -log(u7)
.expr63 <- .expr62^.expr4
.expr65 <- .expr56 * .expr54
.expr66 <- log(.expr62)
.expr71 <- -log(u8)
.expr72 <- .expr71^.expr4
.expr74 <- .expr65 * .expr63
.expr75 <- log(.expr71)
.expr82 <- alpha^8
.expr83 <- 1026576 * .expr82
.expr84 <- .expr2^alpha
.expr85 <- .expr9^alpha
.expr87 <- .expr17^alpha
.expr89 <- .expr26^alpha
.expr91 <- .expr35^alpha
.expr93 <- .expr44^alpha
.expr95 <- .expr53^alpha
.expr97 <- .expr62^alpha
.expr99 <- .expr71^alpha
.expr102 <- -log(u9)
.expr103 <- .expr102^alpha
.expr104 <- .expr84 + .expr85 + .expr87 + .expr89 + .expr91 +
.expr93 + .expr95 + .expr97 + .expr99 + .expr103
.expr105 <- 1/alpha
.expr106 <- .expr104^.expr105
.expr107 <- .expr3 + .expr106
.expr110 <- alpha^7
.expr111 <- 1172700 * .expr110
.expr114 <- 2/alpha
.expr115 <- .expr104^.expr114
.expr116 <- 1 - 3 * .expr106 + .expr115
.expr119 <- alpha^6
.expr120 <- 723680 * .expr119
.expr125 <- 3/alpha
.expr126 <- .expr104^.expr125
.expr127 <- .expr3 + 7 * .expr106 - 6 * .expr115 + .expr126
.expr130 <- alpha^5
.expr131 <- 269325 * .expr130
.expr138 <- 4/alpha
.expr139 <- .expr104^.expr138
.expr140 <- 1 - 15 * .expr106 + 25 * .expr115 - 10 * .expr126 +
.expr139
.expr143 <- alpha^4
.expr144 <- 63273 * .expr143
.expr153 <- 5/alpha
.expr154 <- .expr104^.expr153
.expr155 <- .expr3 + 31 * .expr106 - 90 * .expr115 + 65 *
.expr126 - 15 * .expr139 + .expr154
.expr158 <- alpha^3
.expr159 <- 9450 * .expr158
.expr170 <- 6/alpha
.expr171 <- .expr104^.expr170
.expr172 <- 1 - 63 * .expr106 + 301 * .expr115 - 350 * .expr126 +
140 * .expr139 - 21 * .expr154 + .expr171
.expr175 <- alpha^2
.expr176 <- 870 * .expr175
.expr189 <- 7/alpha
.expr190 <- .expr104^.expr189
.expr191 <- .expr3 + 127 * .expr106 - 966 * .expr115 + 1701 *
.expr126 - 1050 * .expr139 + 266 * .expr154 - 28 * .expr171 +
.expr190
.expr194 <- 45 * alpha
.expr209 <- 8/alpha
.expr210 <- .expr104^.expr209
.expr211 <- 1 - 255 * .expr106 + 3025 * .expr115 - 7770 *
.expr126 + 6951 * .expr139 - 2646 * .expr154 + 462 *
.expr171 - 36 * .expr190 + .expr210
.expr230 <- 9/alpha
.expr231 <- .expr104^.expr230
.expr232 <- .expr3 + 362880 * alpha^9 + .expr83 * .expr107 +
.expr111 * .expr116 + .expr120 * .expr127 + .expr131 *
.expr140 + .expr144 * .expr155 + .expr159 * .expr172 +
.expr176 * .expr191 + .expr194 * .expr211 + 511 * .expr106 -
9330 * .expr115 + 34105 * .expr126 - 42525 * .expr139 +
22827 * .expr154 - 5880 * .expr171 + 750 * .expr190 -
45 * .expr210 + .expr231
.expr234 <- .expr74 * .expr72
.expr259 <- log(.expr102)
.expr261 <- .expr84 * .expr6 + .expr85 * .expr12 + .expr87 *
.expr21 + .expr89 * .expr30 + .expr91 * .expr39 + .expr93 *
.expr48 + .expr95 * .expr57 + .expr97 * .expr66 + .expr99 *
.expr75 + .expr103 * .expr259
.expr264 <- log(.expr104)
.expr266 <- .expr264 * (1/.expr175)
.expr268 <- .expr104^(.expr105 - 1) * (.expr105 * .expr261) -
.expr106 * .expr266
.expr282 <- .expr104^(.expr114 - 1) * (.expr114 * .expr261) -
.expr115 * (.expr264 * (2/.expr175))
.expr301 <- .expr104^(.expr125 - 1) * (.expr125 * .expr261) -
.expr126 * (.expr264 * (3/.expr175))
.expr321 <- .expr104^(.expr138 - 1) * (.expr138 * .expr261) -
.expr139 * (.expr264 * (4/.expr175))
.expr343 <- .expr104^(.expr153 - 1) * (.expr153 * .expr261) -
.expr154 * (.expr264 * (5/.expr175))
.expr367 <- .expr104^(.expr170 - 1) * (.expr170 * .expr261) -
.expr171 * (.expr264 * (6/.expr175))
.expr393 <- .expr104^(.expr189 - 1) * (.expr189 * .expr261) -
.expr190 * (.expr264 * (7/.expr175))
.expr419 <- .expr104^(.expr209 - 1) * (.expr209 * .expr261) -
.expr210 * (.expr264 * (8/.expr175))
.expr452 <- -10 + .expr105
.expr453 <- .expr104^.expr452
.expr455 <- .expr234 * .expr232
.expr464 <- .expr102^.expr4
.expr466 <- .expr455 * .expr453
.expr470 <- E^.expr106
.expr480 <- .expr470 * u1 * u10 * u2 * u3 * u4 * u5 * u6 *
u7 * u8 * u9
.value <- (((((((((((.expr5 * .expr6 * .expr10 + .expr5 *
(.expr10 * .expr12)) * .expr18 + .expr20 * (.expr18 *
.expr21)) * .expr27 + .expr29 * (.expr27 * .expr30)) *
.expr36 + .expr38 * (.expr36 * .expr39)) * .expr45 +
.expr47 * (.expr45 * .expr48)) * .expr54 + .expr56 *
(.expr54 * .expr57)) * .expr63 + .expr65 * (.expr63 *
.expr66)) * .expr72 + .expr74 * (.expr72 * .expr75)) *
.expr232 + .expr234 * (362880 * (9 * .expr82) + (1026576 *
(8 * .expr110) * .expr107 + .expr83 * .expr268) + (1172700 *
(7 * .expr119) * .expr116 + .expr111 * (.expr282 - 3 *
.expr268)) + (723680 * (6 * .expr130) * .expr127 + .expr120 *
(7 * .expr268 - 6 * .expr282 + .expr301)) + (269325 *
(5 * .expr143) * .expr140 + .expr131 * (25 * .expr282 -
15 * .expr268 - 10 * .expr301 + .expr321)) + (63273 *
(4 * .expr158) * .expr155 + .expr144 * (31 * .expr268 -
90 * .expr282 + 65 * .expr301 - 15 * .expr321 + .expr343)) +
(9450 * (3 * .expr175) * .expr172 + .expr159 * (301 *
.expr282 - 63 * .expr268 - 350 * .expr301 + 140 *
.expr321 - 21 * .expr343 + .expr367)) + (870 * (2 *
alpha) * .expr191 + .expr176 * (127 * .expr268 - 966 *
.expr282 + 1701 * .expr301 - 1050 * .expr321 + 266 *
.expr343 - 28 * .expr367 + .expr393)) + (45 * .expr211 +
.expr194 * (3025 * .expr282 - 255 * .expr268 - 7770 *
.expr301 + 6951 * .expr321 - 2646 * .expr343 + 462 *
.expr367 - 36 * .expr393 + .expr419)) + 511 * .expr268 -
9330 * .expr282 + 34105 * .expr301 - 42525 * .expr321 +
22827 * .expr343 - 5880 * .expr367 + 750 * .expr393 -
45 * .expr419 + (.expr104^(.expr230 - 1) * (.expr230 *
.expr261) - .expr231 * (.expr264 * (9/.expr175))))) *
.expr453 + .expr455 * (.expr104^(.expr452 - 1) * (.expr452 *
.expr261) - .expr453 * .expr266)) * .expr464 + .expr466 *
(.expr464 * .expr259))/.expr480 - .expr466 * .expr464 *
(.expr470 * (log(E) * .expr268) * u1 * u10 * u2 * u3 *
u4 * u5 * u6 * u7 * u8 * u9)/.expr480^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
`gumbelCopula.genfunDer.expr` <-
expression((alpha * (-log(u))^alpha)/(u * log(u)), (alpha * (-1 +
alpha - log(u)) * (-log(u))^(-2 + alpha))/u^2)
`gumbelCopula.genfunDer.algr` <-
expression({
.expr1 <- log(u)
.value <- alpha * (-.expr1)^alpha/(u * .expr1)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
}, {
.expr3 <- log(u)
.value <- alpha * (-1 + alpha - .expr3) * (-.expr3)^(-2 +
alpha)/u^2
.grad <- array(0, c(length(.value), 1L), list(NULL, c("s")))
.grad[, "s"] <- 0
attr(.value, "gradient") <- .grad
.value
})
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