HYPERgeometric functions Differential REduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: FD and FS Horn-type hypergeometric functions of three variables

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 F-D of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions F-S of three variables. Both functions are related with one-loop Feynman diagrams. Program summary Program title: HYPERDIRE Catalogue identifier: AEPP_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPP_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 310 No. of bytes in distributed program, including test data, etc.: 7666 Distribution format: tar.gz Programming language: Mathematica Computer: All computers running Mathematica Operating system: All operating systems running Mathematica Classification: 4.4. Catalogue identifier of previous version: AEPP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 2332 Does the new version supersede the previous version?: No. It is an extension to the previous program, which performs reductions of hypergeometric functions F-p(p,) F-1, F-2, F-3 and F-4 Nature of problem: Reduction of hypergeometric functions F-D and F-S to the set of basis functions Solution method: Differential reduction Reasons for new version: New algorithms for the reduction of multivariable Lauricella functions, Horn functions, (hypergeometric functions F-D and F-S) 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 F-D of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions F-S of three variables. Both functions are related with one-loop Feynman diagrams. Running time: Depends on the complexity of problem (C) 2014 Elsevier B.V. All rights reserved.