HYPERgeometric functions DIfferential REduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: [formula omitted] and [formula omitted] Horn-type hypergeometric functions of three variables

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: the first one, FdFunction, for manipulations with Appell hypergeometric functions FD of r variables; and the second one, FsFunction, for manipulations with Lauricella–Saran hypergeometric functions FS of three variables. Both functions are related with one-loop Feynman diagrams. Program summaryProgram title: HYPERDIRECatalogue identifier: AEPP_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPP_v3_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 310No. of bytes in distributed program, including test data, etc.: 7666Distribution format: tar.gzProgramming language: MathematicaComputer: All computers running MathematicaOperating system: All operating systems running MathematicaClassification: 4.4.Catalogue identifier of previous version: AEPP_v1_0Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 2332Does the new version supersede the previous version?: No. It is an extension to the previous program, which performs reductions of hypergeometric functions pFp, F1, F2, F3 and F4Nature of problem: Reduction of hypergeometric functions FD and FS to the set of basis functionsSolution method: Differential reductionReasons for new version: New algorithms for the reduction of multivariable Lauricella functions, Horn functions, (hypergeometric functions FD and FS)Summary of revisions: 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: the first one, FdFunction, for manipulations with Appell hypergeometric functions FD of r variables; and the second one, FsFunction, for manipulations with Lauricella–Saran hypergeometric functions FS of three variables. Both functions are related with one-loop Feynman diagrams.Running time: Depends on the complexity of problem