Epsilon expansion of Appell and Kampé de Fériet functions

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 $\epsilon$-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.

18 pages - Version published in J. Math. Phys. Some corrections and references added

References in corpus (2)

• Series representations for the Stieltjes constants
• Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant

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• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change