HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables

TL;DR

This paper extends the HYPERDIRE project by developing Mathematica packages for differential reduction of Horn-type hypergeometric functions, specifically implementing the Lauricella function F_C of three variables.

Contribution

It introduces a new Mathematica package for the differential reduction of the Lauricella F_C function, expanding tools for hypergeometric function manipulation.

Findings

Successful implementation of differential reduction for Lauricella F_C

Enhanced computational tools for Horn-type hypergeometric functions

Facilitates advanced mathematical and physical research involving hypergeometric functions

Abstract

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function $F_C$ of three variables.