import numpy as np
import scipy.special as sps


def sph_bessel_i(n, x, **kwargs):
    return sps.spherical_in(n, x, **kwargs)


def sph_bessel_k(n, x, **kwargs):
    return 2 / np.pi * sps.spherical_kn(n, x, **kwargs)


def sph_harm(l, m, theta, phi, **kwargs):
    return sps.sph_harm(m, l, phi, theta, **kwargs)


def interaction_coef_C(l, p, x):
    return np.pi / 2 * x * sps.iv(l + 1 / 2, x) * sps.iv(p + 1 / 2, x)


def coefficient_Cpm(l, x):
    return x * sps.kv(l + 1 / 2, x) * sps.iv(l + 1 / 2, x)


def coefficient_Cim(l, x):
    return sps.kv(l + 1 / 2, x) / sps.kv(l + 3 / 2, x)


def coef_C_diff(l, x):
    return 1 / (x * sps.iv(l + 1 / 2, x) * sps.kv(l + 3 / 2, x))