HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters

TL;DR

This paper introduces a new algorithm for expanding hypergeometric functions around half-integer parameters, implemented in HypExp, with applications demonstrated in complex Feynman diagram calculations.

Contribution

The paper presents a novel algorithm for hypergeometric function expansion near half-integers, integrated into HypExp, enhancing computational capabilities for high-loop Feynman diagrams.

Findings

Algorithm successfully expands hypergeometric functions near half-integers.

Implementation in HypExp enables practical calculations in quantum field theory.

Applications include Feynman diagrams with up to four loops.

Abstract

In this article, we describe a new algorithm for the expansion of hypergeometric functions about half-integer parameters. The implementation of this algorithm for certain classes of hypergeometric functions in the already existing Mathematica package HypExp is described. Examples of applications in Feynman diagrams with up to four loops are given.