def METHOD_NAME(rho0, gamma):
    """Converts 3d density into 2d projected density parameter.
    :param rho0:
    :param gamma:
    :return:
    """
    fac = (
        np.sqrt(np.pi)
        * special.gamma(1.0 / 2 * (-1 + gamma))
        / special.gamma(gamma / 2.0)
        * 2
        / (3 - gamma)
        * rho0
    )
    # fac = theta_E**(gamma - 1)
    theta_E = fac ** (1.0 / (gamma - 1))
    return theta_E