Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions

Abstract

Hypergeometric functions provide a useful representation of Feynman diagrams occuring in precision phenomenology. In dimension regularization, the epsilon-expansion of these functions about d=4 is required. We discuss the current status of differential reduction algorithms. As an illustration, we consider the construction of the all-order epsilon-expansion of the Appell hypergeometric function about integer values of the parameters and present an explicit evaluations of the first few terms.

Poster presentation by S.A. Yost at the 34th International Conference on High Energy Physics, Philadelphia, August 2008. 3 pages, no figures, revtex4, slac_one.rtx. Version 4 corrects the arguments of one equation (between eqs. 5 and 6). Version 5 updates the template for ICHEP08