context("elliptic_E")

test_that("phi = pi/2", {
  expect_equal(elliptic_E(pi/2,-1), sqrt(2)*elliptic_E(pi/2,1/2))
  # expect_equal(elliptic_E(pi/2, 0.5),
  #              pi/2*as.complex(gsl::hyperg_2F1(-1/2,1/2,1,0.5))) bug gsl!!
  z <- exp(1i*pi/7)
  expect_equal(elliptic_E(pi/2, 1-1/z),
               elliptic_E(pi/2, 1-z)/sqrt(z))
})

test_that("Representation in terms of elliptic_PI", {
  z <- 7 - 6i
  m <- -3
  expect_equal(elliptic_E(z,m),
               (1-m)*elliptic_PI(z,m,m) + m*sin(2*z)/2/sqrt(1-m*sin(z)^2))
})