A new approach to the epsilon expansion of generalized hypergeometric functions

DOI10.1016/j.cpc.2013.10.001zbMath1348.33005arXiv1302.2423OpenAlexW4300408955MaRDI QIDQ339742

Javier Sesma, David Greynat

Publication date: 11 November 2016

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2423

zbMATH Keywords

hypergeometric functionsAppell functionsderivatives of Pochhammer symbolsepsilon expansionKampé de Fériet functions

Mathematics Subject Classification ID

Appell, Horn and Lauricella functions (33C65)

Related Items (9)

Hypergeometric structures in Feynman integrals ⋮ Derivatives of Horn hypergeometric functions with respect to their parameters ⋮ \texttt{MultiHypExp}: a \textsc{Mathematica} package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms ⋮ \(\epsilon\)-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus ⋮ Derivatives of any Horn-type hypergeometric functions with respect to their parameters ⋮ Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions ⋮ Two-loop Feynman integrals for ϕ4 theory with long-range correlated disorder ⋮ Analytic periods via twisted symmetric squares ⋮ Hypergeometric Functions and Feynman Diagrams

Uses Software

• DLMF

Cites Work

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• Hypergeometric functions
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• \(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections
• SecDec: A general program for sector decomposition
• The special functions and their approximations. Vol. I, II
• Nielsen’s Generalized Polylogarithms
• Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
• Expansion around half-integer values, binomial sums, and inverse binomial sums
• New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams

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