A NEW APPROACH TO THE TAYLOR EXPANSION OF MULTILOOP FEYNMAN DIAGRAMS

We present a new method for the Taylor expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function f or the coefficients of the small momentum expansion of an arbitrary di agram. The method is applicable for the expansion with respect to all or a subset of external momenta. The coefficients of the expansion are obtained by applying a differential operator to a given integral with shifted value of the space-time dimension d and the expansion momenta set equal to zero, Integrals with changed d are evaluated by using th e generalized recurrence relations recently proposed [O.V. Tarasov, Co nnection between Feynman integrals having different values of the spac e-time dimension, preprint DESY 96-068, JINR E2-96-62 (hep-th/9606018) , to be published in Phys. Rev. D 54, No, 10 (1996)]. We show how the method works for one- and two-loop integrals. It is also illustrated t hat our method is simpler and more efficient than others.