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On the evaluation of the Appell F2 double hypergeometric function

Ananthanarayan, B and Bera, S and Friot, S and Marichev, O and Pathak, T (2023) On the evaluation of the Appell F2 double hypergeometric function. In: Computer Physics Communications, 284 .

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Official URL: https://doi.org/10.1016/j.cpc.2022.108589


The transformation theory of the Appell F2(a,b1,b2;c1,c2;x,y) double hypergeometric function is developed to obtain a set of series representations of F2 which provide an efficient way to evaluate F2 for real values of its arguments x and y and generic complex values of its parameters a,b1,b2,c1 and c2 (i.e. in the nonlogarithmic case). This study rests on a classical approach where the usual double series representation of F2 and other double hypergeometric series that appear in the intermediate steps of the calculations are written as infinite sums of one variable hypergeometric series, such as the Gauss F12 or the F23, various linear transformations of the latter being then applied to derive known and new formulas. Use of the three well-known Euler transformations of F2 on these results allows us to obtain a total of 44 series which form the basis of the Mathematica package AppellF2.wl, dedicated to the evaluation of F2. A brief description of the package and of the numerical analysis that we have performed to test it is also presented. Program summary: Program Title: AppellF2.wl CPC Library link to program files: https://doi.org/10.17632/n9v6bwpsyd.1 Licensing provisions: GPLv3 Programming language: Wolfram Mathematica version 11.3 and beyond Nature of problem: Numerical evaluation of the double hypergeometric Appell F2 function for real values of its variables and generic complex values of its Pochhammer parameters Solution method: Mathematica implementation of a set of transformation formulas of the Appell F2 function © 2022 Elsevier B.V.

Item Type: Journal Article
Publication: Computer Physics Communications
Publisher: Elsevier B.V.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Function evaluation; Linear transformations, Appell's functions; Complex values; Double hypergeometric function; Horn function; Hypergeometric functions; Hypergeometric series; Mathematica; Numerical evaluation; Real values; Series representations, Numerical methods
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 27 Jan 2023 07:16
Last Modified: 27 Jan 2023 07:16
URI: https://eprints.iisc.ac.in/id/eprint/79531

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