import math


def nu_e(n_n, n_e, T_e):
    """approximate calculation of electron collision frequency from Kelly 89

    Parameters
    ----------
    n_n : (float)
        neutral density cm-3
    n_e : (float)
        electron density cm-3
    T_e : (float)
        electron temperature K
    """
    nu_e_n = 5.4 * 10**(-10) * n_n * T_e**(1/2)
    nu_e_i = (34 + 4.18 * math.log(T_e**3 / n_e)) * n_e * T_e**(-3/2)
    return nu_e_n + nu_e_i