HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables

TL;DR

This paper introduces HYPERDIRE, a Mathematica package that enables differential reduction of Horn hypergeometric functions of two variables, covering 30 functions for advanced mathematical analysis.

Contribution

It provides the first comprehensive Mathematica-based tool for differential reduction of all Horn hypergeometric functions of two variables.

Findings

Supports 30 Horn hypergeometric functions of two variables

Facilitates symbolic manipulation and reduction

Enhances computational capabilities for hypergeometric functions

Abstract

HYPERDIRE is a project devoted to the creation of a set of Mathematica-based programs for the differential reduction of hypergeometric functions. The current version allows for manipulations involving the full set of Horn-type hypergeometric functions of two variables, including 30 functions.