David Greynat, Javier Sesma, Grégory Vulvert
Published 2013-10-29, updated 2014-03-28Version 3
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 $\varepsilon$-expansion of functions of the hypergeometric class. The procedure is applied to several Appell and Kamp\'e de F\'eriet 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.
Comments: 18 pages - Version published in J. Math. Phys. Some corrections and references added
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