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### E[ log(Y+1) ]
k0 <- function(lambda,delta, N=NULL, eps=sqrt(.Machine$double.eps)){
if(is.null(N)){
B = lambda * 2^delta * log(2)
re <- 1
TAU <- tau(lambda,delta, N, eps)
K = B/TAU
j <- 1
while(re > eps){
B = lambda/(j+1) * (log(j+2)/log(j+1)) * ((j+2)/(j+1))^delta * B
K = K + B/TAU
j=j+1
re <- B/K
}
}else{
x <- 0:N
lnum <- delta * log(x+1) + x * log(lambda)
lden <- lgamma(x+1) + log(tau(lambda, delta, N, eps))
K <- sum(log(x+1)*exp(lnum-lden))
}
return(K)
}
kapa <- Vectorize(k0, c('lambda','delta'))
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