HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4

TL;DR

HYPERDIRE is a Mathematica package designed to facilitate the differential reduction of various hypergeometric functions, including generalized and Appell functions, aiding symbolic manipulation in mathematical research.

Contribution

The paper introduces HYPERDIRE, a new software package that automates differential reduction of hypergeometric functions within Mathematica, covering both univariate and multivariate cases.

Findings

Provides tools for differential reduction of pFq functions

Includes capabilities for Appell hypergeometric functions F1-F4

Enhances symbolic computation in 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 includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions_{p+1}F_p, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F_1,F_2,F_3,F_4 of two variables.