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We investigate the affine perturbation series of the deflection angle of aray near the photon sphere of an extreme Reissner-Nordstr\"{o}m black hole. Wecompare the 0th and 1st orders of the affine perturbation series with thedeflection angle in a strong deflection limit. We conclude that the 0th orderof the affine perturbation series is more accurate than the deflection angle inthe strong deflection limit and that we should improve astrong-deflection-limit analysis by using the 0th order of the affineperturbation series.

Affine perturbation series of the deflection angle of a ray near the photon sphere of a Reissner-Nordstr\"{o}m black hole