def METHOD_NAME(SED1, SED2, bandpass):
    index = -0.2
    # analytic moment differences
    x1 = np.union1d(bandpass.wave_list, SED1.wave_list)
    x1 = x1[(x1 <= bandpass.red_limit) & (x1 >= bandpass.blue_limit)]
    x2 = np.union1d(bandpass.wave_list, SED2.wave_list)
    x2 = x2[(x2 <= bandpass.red_limit) & (x2 >= bandpass.blue_limit)]
    num1 = np.trapz((x1/500)**(2*index) * bandpass(x1) * SED1(x1), x1)
    num2 = np.trapz((x2/500)**(2*index) * bandpass(x2) * SED2(x2), x2)
    den1 = SED1.calculateFlux(bandpass)
    den2 = SED2.calculateFlux(bandpass)
    r2_1 = num1/den1
    r2_2 = num2/den2
    dr2byr2_analytic = (r2_1 - r2_2) / r2_1
    return dr2byr2_analytic