PUB - Publikationen an der Universität Bielefeld

A difference equation w.r.t. space-time dimension $d$ for $n$-point one-loopintegrals with arbitrary momenta and masses is introduced and a solutionpresented. The result can in general be written as multiple hypergeometricseries with ratios of different Gram determinants as expansion variables.Detailed considerations for $2-,3-$ and $4-$point functions are given. For the$2-$ point function we reproduce a known result in terms of the Gausshypergeometric function $_2F_1$. For the $3-$point function an expression interms of $_2F_1$ and the Appell hypergeometric function $F_1$ is given. For the$4-$point function a new representation in terms of $_2F_1$, $F_1$ and theLauricella-Saran functions $F_S$ is obtained. For arbitrary $d=4-2\epsilon$,momenta and masses the $2-,3-$ and $4-$point functions admit a simple one-foldintegral representation. This representation will be useful for the calculationof contributions from the $\epsilon-$ expansion needed in higher orders ofperturbation theory. Physically interesting examples of $3-$ and $4-$pointfunctions occurring in Bhabha scattering are investigated.