def test_interrelations_k_exact(self):
n = 7
x = 5.746161870059113
left = np.complex(sph_kn_exact(n, x))
right = np.complex((-1)**(n + 1) * pi / 2 *
(sph_i1n_exact(n, x) - sph_i2n_exact(n, x)))
assert_allclose(left, right)
def test_sph_i22_exact(self):
x = 6.916886515975276
desired = (1 / x + 3 / x ** 3) * np.cosh(x) - 3 / x ** 2 * np.sinh(x)
actual = np.complex(sph_i2n_exact(2, x))
assert_allclose(actual, desired)
def test_sph_i21_exact(self):
x = 11.070885074673603
desired = -np.cosh(x) / x ** 2 + np.sinh(x) / x
actual = np.complex(sph_i2n_exact(1, x))
assert_allclose(actual, desired)
def test_sph_i20_exact(self):
x = 5.807556326907072
desired = np.cosh(x) / x
actual = np.complex(sph_i2n_exact(0, x))
assert_allclose(actual, desired)
def test_interrelations_i2_exact(self):
n = 9
x = 6.083765036260925
left = np.complex(sph_i2n_exact(n, x))
right = np.complex(mpc(0, 1) ** (-n - 1) * sph_yn_exact(n, 1j * x))
assert_allclose(left, right)
def test_interrelations_k_exact(self):
n = 7
x = 5.746161870059113
left = np.complex(sph_kn_exact(n, x))
right = np.complex((-1) ** (n + 1) * pi / 2 * (sph_i1n_exact(n, x) - sph_i2n_exact(n, x)))
assert_allclose(left, right)
def test_sph_i22_exact(self):
x = 6.916886515975276
desired = (1 / x + 3 / x**3) * np.cosh(x) - 3 / x**2 * np.sinh(x)
actual = np.complex(sph_i2n_exact(2, x))
assert_allclose(actual, desired)
def test_sph_i21_exact(self):
x = 11.070885074673603
desired = -np.cosh(x) / x**2 + np.sinh(x) / x
actual = np.complex(sph_i2n_exact(1, x))
assert_allclose(actual, desired)
def test_sph_i20_exact(self):
x = 5.807556326907072
desired = np.cosh(x) / x
actual = np.complex(sph_i2n_exact(0, x))
assert_allclose(actual, desired)
def test_interrelations_i2_exact(self):
n = 9
x = 6.083765036260925
left = np.complex(sph_i2n_exact(n, x))
right = np.complex(mpc(0, 1)**(-n - 1) * sph_yn_exact(n, 1j * x))
assert_allclose(left, right)