import math


def tau_polinomyal_coefficients(z):
    """
    Coefficients (z-dependent) for the log(tau) formula from
    Raiteri C.M., Villata M. & Navarro J.F., 1996, A&A 315, 105-115

    """
    log_z = math.log10(z)
    log_z_2 = log_z ** 2

    a0 = 10.13 + 0.07547 * log_z - 0.008084 * log_z_2
    a1 = -4.424 - 0.7939 * log_z - 0.1187 * log_z_2
    a2 = 1.262 + 0.3385 * log_z + 0.05417 * log_z_2

    return [a0, a1, a2]