Computer Algebra and Hypergeometric Structures for Feynman Integrals

TL;DR

This paper discusses advanced computer algebra techniques for calculating series solutions of differential equations, especially those involving hypergeometric functions relevant to Feynman integrals.

Contribution

It introduces new computer algebra methods for handling multivariate series solutions with hypergeometric structures in the context of Feynman integrals.

Findings

Supports calculations of multivariate series solutions

Handles hypergeometric products and nested sums

Applicable to parameter Feynman integrals

Abstract

We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by hypergeometric products and more generally by indefinite nested sums defined over such products. Special cases are hypergeometric structures such as Appell-functions or generalizations of them that arise frequently when dealing with parameter Feynman integrals.