Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions

Abstract

Useful expressions of the derivatives, to any order, of Pochhammer and reciprocal Pochhammer symbols with respect to their arguments are presented. They are building blocks of a procedure, recently suggested, for obtaining the ɛ-expansion of functions of the hypergeometric class related to Feynman integrals. The procedure is applied to some examples of such kind of functions taken from the literature.