def k_AP(k_obs, mu_obs, alpha_perp, alpha_par):
    """
    Return the `true` k values, given an observed (k, mu).

    This corresponds to the `k` to evaluate P(k,mu) at when including
    the AP effect
    """
    F = alpha_par / alpha_perp
    if F != 1.0:
        return k_obs / alpha_perp * (1 + mu_obs ** 2 * (1.0 / F ** 2 - 1)
            ) ** 0.5
    else:
        return k_obs / alpha_perp
