HYPERgeometric functions DIfferential REduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: FD F D and FS F S 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 FD F D of r r variables; and the second one, FsFunction, for manipulations with LauricellaSaran hypergeometric functions FS F S of three variables. Both functions are related with one-loop Feynman diagrams. 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, Queens 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 pFp p F p , F1 F 1 , F2 F 2 , F3 F 3 and F4 F 4 Nature of problem:  Reduction of hypergeometric functions FD F D and FS 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 FD F D and FS 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 FD F D of r r variables; and the second one, FsFunction, for manipulations with LauricellaSaran hypergeometric functions FS F S of three variables. Both functions are related with one-loop Feynman diagrams. Running time: Depends on the complexity of problem
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