Nothing
context("elliptic_F")
test_that("phi = pi/2", {
expect_equal(elliptic_F(pi/2,-1), as.complex(gamma(1/4)^2/4/sqrt(2*pi)))
expect_equal(elliptic_F(pi/2,1/2),
as.complex(8*pi^(3/2)/gamma(-1/4)^2))
expect_equal(elliptic_F(pi/2, 0.5),
pi/2*as.complex(gsl::hyperg_2F1(1/2,1/2,1,0.5)))
z <- 5+2i
expect_equal(sqrt(1-z)*elliptic_F(pi/2,z),
elliptic_F(pi/2, z/(z-1)))
expect_equal(elliptic_F(pi/2,1/z),
sqrt(z)*(elliptic_F(pi/2,z) - 1i*elliptic_F(pi/2,1-z)))
})
test_that("Representation in terms of elliptic_PI", {
z <- 7 - 6i
m <- -3
expect_equal(elliptic_F(z,m), elliptic_PI(z,0,m))
})
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