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F,(a) is defined as the contribution of the one-fermion-loop diagrams to the divergent part of the photon propagator in massless quantum electrodynamics. T o sixth order, the perturbation expansion of F,(a) has rational coefficients: F,(a) = ( 2 / 3 ) ( a / 2~) + ( a / 2~) * -(1/4)(a/2n)l + .. .. It is not known whether the next term in this series is a rational number; however, we propose a new method, which uses integration by parts, for evaluating Feynman integrals which give rational numbers. Using this method we easily rederive the first three terms in the series for F,(a) and three other two-loop integrals, including the fourth-order correction to the vertex function r P ( p , p ) . We believe that our new integration techniques are powerful enough to evaluate the fourth term in the series for Fl(a) if it is a rational number.

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