Hypergeometric functions with rational arguments

TL;DR

This paper discusses the expansion of hypergeometric functions with rational parameters, especially half-integers, introduces an algorithm implemented in Mathematica for such expansions, and applies it to multi-loop Feynman diagrams and a three-loop HQET integral.

Contribution

It presents a new algorithm for expanding hypergeometric functions with rational parameters and its implementation in the HypExp Mathematica package, enabling new results in quantum field theory calculations.

Findings

Derived new results for multi-loop Feynman diagrams

Provided a new formulation of a conjecture in HQET

Enhanced computational tools for hypergeometric function expansions

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.