HYPERDIRE—HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function [formula omitted] of three variables

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 FC of three variables. Program summaryProgram title: HYPERDIRECatalogue identifier: AEPP_v4_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPP_v4_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 243461No. of bytes in distributed program, including test data, etc.: 61610782Distribution format: tar.gzProgramming language: Mathematica.Computer: All computers running Mathematica.Operating system: Operating systems running Mathematica.Classification: 4.4.Does the new version supersede the previous version?: No, it significantly extends the previous version.Nature of problem:Reduction of hypergeometric function FC of three variables to a set of basis functions.Solution method:Differential reduction.Reasons for new version:The extension package allows the user to handle the Lauricella function FC of three variables.Summary of revisions:The previous version goes unchanged.Running time:Depends on the complexity of the problem.