Hypergeometric functions with rational arguments

Abstract

We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about half-integer parameters are described. The algorithm is implemented in the Mathematica package HypExp, by means of which we derive (partially new) results of selected multi-loop Feynman diagrams. Moreover, we give a new formulation of a conjecture in the context of a three-loop master integral in HQET.