Nothing
context("elliptic_Z")
test_that("Representation in terms of elliptic_PI", {
z <- 7 - 6i
m <- -3
expect_equal(
elliptic_Z(z,m),
(1-m)*elliptic_PI(z,m,m) + m*sin(2*z)/2/sqrt(1-m*sin(z)^2) -
elliptic_E(pi/2,m)/elliptic_F(pi/2,m)*elliptic_PI(z,0,m)
)
})
test_that("Special values", {
z <- -1 + 8i
expect_equal(elliptic_Z(z,0), as.complex(0))
expect_equal(elliptic_Z(z,1), sin(z))
expect_equal(elliptic_Z(0, 2+2i), as.complex(0))
expect_equal(elliptic_Z(5*pi/2, 2+2i), as.complex(0))
})
test_that("Periodicity", {
z <- -5 + 3i
m <- -4
expect_equal(
elliptic_Z(z,m),
elliptic_Z(z + 7*pi, m)
)
})
test_that("Symmetry", {
z <- -5 + 3i
m <- -4 - 9i
expect_equal(
elliptic_Z(Conj(z),Conj(m)),
Conj(elliptic_Z(z,m))
)
})
test_that("Parity", {
z <- -5 + 3i
m <- -4 - 9i
expect_equal(
elliptic_Z(-z,m),
-elliptic_Z(z,m)
)
})
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