Olsson.wl: A Mathematica Package for the Computation of Linear Transformations of Multivariable Hypergeometric Functions

Ananthanarayan, B and Bera, S and Friot, S and Pathak, T (2024) Olsson.wl: A Mathematica Package for the Computation of Linear Transformations of Multivariable Hypergeometric Functions. In: 25th DAE-BRNS High Energy Physics Symposium, HEPS 2022, 12 December 2022through 16 December 2022, IISER Mohali, pp. 738-740.

PDF spi_pro_phy_304_2024 - Published Version Restricted to Registered users only Download (512kB) | Request a copy

Abstract

We present the Olsson.wl Mathematica package which aims to find linear transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson in J. Math. Phys. 5, 420 (1964) to derive the analytic continuations of the Appell F1 double hypergeometric series from the linear transformations of the Gauss2F1 hypergeometric function. We provide a brief description of Olsson�s method and demonstrate the commands of the package, along with examples. We also provide a companion package, called ROC2.wl and dedicated to the derivation of the regions of convergence of double hypergeometric series. As applications, we show the usefulness of the package in finding the analytic continuations of Feynman integrals via their hypergeometric function representation. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

Item Type:	Conference Paper
Publication:	Springer Proceedings in Physics
Publisher:	Springer Science and Business Media Deutschland GmbH
Additional Information:	The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH.
Keywords:	Functional analysis, Analytic continuation; Feynman integrals; Function representations; Hypergeometric functions; Hypergeometric series; Mathematica packages; Multi variables; Region of convergence; S-method, Linear transformations
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	10 Sep 2024 09:34
Last Modified:	10 Sep 2024 09:34
URI:	http://eprints.iisc.ac.in/id/eprint/86045

Actions (login required)

View Item