Epsilon expansion of Appell and Kamp\'e de F\'eriet functions

Understand

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.