def spectrum_matsubara_approx(w, ck, vk):
    """
    Calculates the approximate Matsubara correlation spectrum
    from ck and vk.
    
    Parameters
    ==========

    w: np.ndarray
        A 1D numpy array of frequencies.
    
    ck: float
        The coefficient of the exponential function.

    vk: float
        The frequency of the exponential function.
    """
    return ck*2*(vk)/(w**2 + vk**2)