Nothing
context("Herz's relations")
test_that("Herz's relation for 1F1", {
X <- toeplitz(c(3, 2, 1)) / 100
o1 <- hypergeomPFQ(m = 15, a = 2, b = 3, x = X)
o2 <- exp(sum(diag(X))) * hypergeomPFQ(m = 15, a = 3 - 2, b = 3, x = -X)
expect_equal(o1, o2)
#
X <- toeplitz(c(3i, 2, 1)) / 100
o1 <- hypergeomPFQ(m = 15, a = 2i, b = 3, x = X)
o2 <- exp(sum(diag(X))) * hypergeomPFQ(m = 15, a = 3 - 2i, b = 3, x = -X)
expect_equal(o1, o2)
})
test_that("Herz's relation for 2F1", {
X <- toeplitz(c(3, 2, 1)) / 100
o1 <- hypergeomPFQ(m = 15, a = c(1, 2i), b = 3, x = X)
o2 <- det(diag(3) - X)^(-2i) *
hypergeomPFQ(15, a = c(3 - 1, 2i), b = 3, -X %*% solve(diag(3) - X))
expect_equal(o1, o2)
#
X <- toeplitz(c(3, 2, 1)) / 100
o1 <- hypergeomPFQ(m = 15, a = c(1, 2), b = 3, x = X)
o2 <- det(diag(3) - X)^(-2) *
hypergeomPFQ(15, a = c(3 - 1, 2), b = 3, -X %*% solve(diag(3) - X))
expect_equal(o1, o2)
#
X <- toeplitz(c(3i, 2, 1)) / 100
o1 <- hypergeomPFQ(m = 15, a = c(1, 2i), b = 3, x = X)
o2 <- EigenR::Eigen_det(diag(3) - X)^(-2i) *
hypergeomPFQ(15, a = c(3 - 1, 2i), b = 3, -X %*% solve(diag(3) - X))
expect_equal(o1, o2)
#
X <- toeplitz(c(3i, 2, 1)) / 100
o1 <- hypergeomPFQ(m = 15, a = c(1, 2), b = 3, x = X)
o2 <- EigenR::Eigen_det(diag(3) - X)^(-2) *
hypergeomPFQ(15, a = c(3 - 1, 2), b = 3, -X %*% solve(diag(3) - X))
expect_equal(o1, o2)
})
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