Epsilon expansion of Appell and Kampé de Fériet functions

2013/10/29 by David Greynat, Greynat, David, J. Sesma +3
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1310.7700

openalex publication_date 2013/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The decomposition in partial fractions of the quotient of Pochhammer symbols improves considerably a method, suggested in a precedent paper, which allows one to obtain the ε-expansion of functions of the hypergeometric class. The procedure is applied to several Appell and Kampé de Fériet functions considered in the literature. Explicit expressions and interesting properties of the derivatives of the Pochhammer and reciprocal Pochhammer symbols, which are essential elements in the procedure, are given in an appendix.

Citations

• Series representations for the Stieltjes constants

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