def limb_darkening_old(mu,u1,u2):
    """Evaluate quadratic limb darkening, taken from de Mooij 2017,
    (https://arxiv.org/pdf/1709.00680.pdf). Provide the mu-angle of grid cell i,j
    and multiply the resulting weight against spectrum i,j.

    This formula has been updated for a
    potential typo from (1-mu)**2 to (1-mu**2)

        Parameters
        ----------
        mu : float, np.array()
            the cosine of the angle between the line of sight and the stellar
            surface vertical.
        u1,u2: float,
            Linear and quadratic limb-darkening coefficients.
        Returns
        -------
        w: float
            The weight, <= 1.
    """
    w=(1-u1*(1-mu)-u2*(1-mu**2))

    return(w)