HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
Vladimir V. Bytev (Dubna, JINR), Mikhail Yu. Kalmykov (Hamburg U.,, Inst. Theor. Phys. II, Dubna, JINR), Bernd A.Kniehl (Hamburg U., Inst., Theor. Phys. II)

TL;DR
HYPERDIRE is a Mathematica package designed to facilitate the differential reduction of various hypergeometric functions, including generalized and Appell functions, aiding symbolic manipulation in mathematical research.
Contribution
The paper introduces HYPERDIRE, a new software package that automates differential reduction of hypergeometric functions within Mathematica, covering both univariate and multivariate cases.
Findings
Provides tools for differential reduction of pFq functions
Includes capabilities for Appell hypergeometric functions F1-F4
Enhances symbolic computation in hypergeometric functions
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: one, pfq, is relevant for manipulations of hypergeometric functions_{p+1}F_p, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F_1,F_2,F_3,F_4 of two variables.
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