Olsson.wl & ROC2.wl: Mathematica packages for transformations of multivariable hypergeometric functions & regions of convergence for their series representations in the two variables case

Ananthanarayan, B and Bera, S and Friot, S and Pathak, T (2024) Olsson.wl & ROC2.wl: Mathematica packages for transformations of multivariable hypergeometric functions & regions of convergence for their series representations in the two variables case. In: Computer Physics Communications, 300 .

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Abstract

We present the Olsson.wl Mathematica package which aims to find transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson 1 (1964) to derive the analytic continuations of the Appell F1 double hypergeometric series using the linear transformations of the Gauss F12 hypergeometric function. We provide a brief description of the method of Olsson and demonstrate the use of the commands of the Olsson.wl package using some examples that are presented in the text and in some ancillary Mathematica notebooks. In particular, we reproduce various results of the literature on multivariable hypergeometric functions and show practical applications of this package in the derivation of novel formulas. In the context of high energy physics, we also demonstrate how it can be used to disentangle some known results about the analytic continuation of some series representations of the one-loop pentagon in multi-Regge kinematics and D=6�2ϵ. We also provide a companion package, called ROC2.wl, which is dedicated to the derivation of the regions of convergence of double hypergeometric series. This package can be used independently of Olsson.wl. Program summary: Program Title: Olsson.wl CPC Library link to program files: https://doi.org/10.17632/gc63xzwzz5.1 Licensing provisions: GNU General Public License v3.0. Programming language: Wolfram Mathematica version 11.3 and beyond. Nature of problem: To find the transformation formulas of multivariable hypergeometric series appearing in Feynman integral calculus. Solution method: Mathematica implementation of the method of Olsson 1. The method uses the transformation theory of lower variable hypergeometric functions to find the transformation formulas of higher variable hypergeometric functions. Companion package: ROC2.wl, which is a Mathematica package used inside Olsson.wl and can also be used as a standalone package. The package is used to find the region of convergence of double hypergeometric functions, using Horn's theorem. © 2024 Elsevier B.V.

Item Type:	Journal Article
Publication:	Computer Physics Communications
Publisher:	Elsevier B.V.
Additional Information:	The copyright for this article belongs to Elsevier B.V.
Keywords:	Functional analysis; High energy physics; Integral equations; Matrix algebra; Quantum theory, Analytic continuation; Appell's functions; Feynman integrals; Hypergeometric functions; Hypergeometric series; Mathematica; Mathematica packages; Multi variables; Region of convergence; Series representations, Linear transformations
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	21 May 2024 05:11
Last Modified:	21 May 2024 05:11
URI:	https://eprints.iisc.ac.in/id/eprint/84743

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