Epsilon-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus

Bera, S (2024) Epsilon-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus. In: 25th DAE-BRNS High Energy Physics Symposium, HEPS 2022, 12 December 2022through 16 December 2022, IISER Mohali, pp. 741-742.

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Abstract

We present a new methodology to perform the ϵ-expansion of hypergeometric functions with linear ϵ-dependent Pochhammer parameters in any number of variables. Our approach allows one to perform Taylor as well as Laurent series expansion of multivariable hypergeometric functions. Each of the coefficients of ϵ in the series expansion is expressed as a linear combination of multivariable hypergeometric functions with the same domain of convergence as that of the original hypergeometric function thereby providing a closed system of expressions. We present illustrative examples of hypergeometric functions in one, two, and three variables which are typical of Feynman integral calculus. © 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 the Publisher.
Keywords:	Closed systems; Epsilon expansion; Feynman integrals; Hypergeometric functions; Integral calculus; Laurent series expansion; Linear combinations; Multi variables; Taylor's series expansion, Integral equations
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	03 Sep 2024 04:28
Last Modified:	03 Sep 2024 04:28
URI:	http://eprints.iisc.ac.in/id/eprint/86041

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