HYPERDIRE, HYPERgeometric functions DIfferential REduction: MATHEMATICA-based packages for differential reduction of generalized hypergeometric functions pFp−1,F1,F2,F3,F4pFp−1,F1,F2,F3,F4

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: one, pfq, is relevant for manipulations of hypergeometric functions p+1Fpp+1Fp, and the other, AppellF1F4, for manipulations with Appell hypergeometric functions F1,F2,F3,F4F1,F2,F3,F4 of two variables.Program summaryProgram title: HYPERDIRECatalogue identifier: AEPP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenceNo. of lines in distributed program, including test data, etc.: 3428No. of bytes in distributed program, including test data, etc.: 394 247Distribution format: tar.gzProgramming language: Mathematica.Computer: All computers running Mathematica.Operating system: Operating systems running Mathematica.Classification: 4.4.Nature of problem:   Reduction of hypergeometric functions pFp−1,F1,F2,F3,F4pFp−1,F1,F2,F3,F4 to sets of basis functions.Solution method: Differential reductionRunning time: Dependent on the complexity of problem. The examples provided take less than a minute to run.