def test_interrelations_i1_bessel(self):
n = 3
x = 1.9513017144556937
left = np.complex(sph_i1n_bessel(n, x))
right = np.complex(mpc(0, 1) ** (-n) * sph_jn_bessel(n, 1j * x))
assert_allclose(left, right)
def test_interrelations_h1_bessel(self):
n = 6
x = 8.160875740148962
left = np.complex(sph_h1n_bessel(n, x))
right = np.complex(sph_jn_bessel(n, x) + 1j * sph_yn_bessel(n, x))
assert_allclose(left, right)
def test_interrelations_h2_bessel(self):
n = 5
x = 2.826012588052626
left = np.complex(sph_h2n_bessel(n, x))
right = np.complex(sph_jn_bessel(n, x) - 1j * sph_yn_bessel(n, x))
assert_allclose(left, right)
def test_sph_j1_bessel(self):
x = 1.3
desired = np.sin(x) / x ** 2 - np.cos(x) / x
actual = np.complex(sph_jn_bessel(1, x))
assert_allclose(actual, desired)
def test_sph_j2_bessel(self):
x = 24.5
desired = (-1.0 / x + 3 / x ** 3) * np.sin(x) - 3 / x ** 2 * np.cos(x)
actual = np.complex(sph_jn_bessel(2, x))
assert_allclose(actual, desired)
def test_interrelations_i1_bessel(self):
n = 3
x = 1.9513017144556937
left = np.complex(sph_i1n_bessel(n, x))
right = np.complex(mpc(0, 1)**(-n) * sph_jn_bessel(n, 1j * x))
assert_allclose(left, right)
def test_sph_j0_bessel(self):
x = 52
desired = np.sin(x) / x
actual = np.complex(sph_jn_bessel(0, x))
assert_allclose(actual, desired)
def test_interrelations_h2_bessel(self):
n = 5
x = 2.826012588052626
left = np.complex(sph_h2n_bessel(n, x))
right = np.complex(sph_jn_bessel(n, x) - 1j * sph_yn_bessel(n, x))
assert_allclose(left, right)
def test_interrelations_h1_bessel(self):
n = 6
x = 8.160875740148962
left = np.complex(sph_h1n_bessel(n, x))
right = np.complex(sph_jn_bessel(n, x) + 1j * sph_yn_bessel(n, x))
assert_allclose(left, right)
def test_sph_j2_bessel(self):
x = 24.5
desired = (-1.0 / x + 3 / x**3) * np.sin(x) - 3 / x**2 * np.cos(x)
actual = np.complex(sph_jn_bessel(2, x))
assert_allclose(actual, desired)
def test_sph_j1_bessel(self):
x = 1.3
desired = np.sin(x) / x**2 - np.cos(x) / x
actual = np.complex(sph_jn_bessel(1, x))
assert_allclose(actual, desired)
def test_sph_j0_bessel(self):
x = 52
desired = np.sin(x) / x
actual = np.complex(sph_jn_bessel(0, x))
assert_allclose(actual, desired)
