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We present analytic results for one of two types of planar QED two-loopintegrals for $\mu e$ scattering including finite lepton masses. Noapproximations are made, such that the results are valid not only in the limitof a small electron mass. The results are expressed in terms of multiplepolylogarithms with algebraic function arguments in a representation whichallows for fast numerical evaluation in the physical phase-space.

Planar two-loop integrals for $\mathbf{\mu e}$ scattering in QED with finite lepton masses