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Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions. (English) Zbl 1292.81102

Summary: 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 \(\epsilon\)-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.{
©2014 American Institute of Physics}

MSC:

81T18 Feynman diagrams
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
33C65 Appell, Horn and Lauricella functions

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DLMF; Nestedsums
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