MultiHypExp: A MATHEMATICA package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms

Bera, S (2024) MultiHypExp: A MATHEMATICA package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms. In: Computer Physics Communications, 297 .

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Abstract

We present the MATHEMATICA package MultiHypExp that allows for the expansion of multivariate hypergeometric functions (MHFs), especially those likely to appear as solutions of multi-loop, multi-scale Feynman integrals, in the dimensional regularization parameter. The series expansion of MHFs can be carried out around integer values of parameters to express the series coefficients in terms of multiple polylogarithms. The package uses a modified version of the algorithm prescribed in 1. In the present work, we relate a given MHF to a Taylor series expandable MHF by a differential operator. The Taylor expansion of the latter MHF is found by first finding the associated partial differential equations (PDEs) from its series representation. We then bring the PDEs to the Pfaffian system and further to the canonical form, and solve them order by order in the expansion parameter using appropriate boundary conditions. The Taylor expansion so obtained and the differential operators are used to find the series expansion of the given MHF. We provide examples to demonstrate the algorithm and to describe the usage of the package, which can be found in this url. Program summary: Program Title: MultiHypExp.wl version 1.0 CPC Library link to program files: https://doi.org/10.17632/zxwkx38y7b.1 Developer's repository link: https://github.com/souvik5151/MultiHypExp Licensing provisions: GNU General Public License 3 Programming language: Wolfram Mathematica version 11.3 or higher External routines/libraries: HolonomicFunctions, CANONICA, HYPERDIRE, PolyLogTools, HPL Nature of problem: Obtaining the series expansion of multivariate hypergeometric functions around integer values of Pochhammer parameters in terms of multiple polylogarithms Solution method: Mathematica implementation of a modified version of the algorithm prescribed in Nucl. Phys. B 989 (2023) 116145. © 2023 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:	Boundary conditions; HTTP; Mathematical operators, Differential operators; Feynman integrals; Hypergeometric functions; Integer values; Multiple polylogarithm; Mutivariate hypergeometric function; Pfaffian; Pfaffian system; Polylogarithms; Series expansion, Taylor series
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	01 Mar 2024 06:22
Last Modified:	01 Mar 2024 06:22
URI:	https://eprints.iisc.ac.in/id/eprint/83881

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