A new approach to the epsilon expansion of generalized hypergeometric functions

Understand

Assumed that the parameters of a generalized hypergeometric function depend linearly on a small variable $\varepsilon$, the successive derivatives of the function with respect to that small variable are evaluated at $\varepsilon=0$ to obtain the coefficients of the $\varepsilon$-expansion of the function.

• The procedure, quite naive, benefits from simple explicit expressions of the derivatives, to any order, of the Pochhammer and reciprocal Pochhammer symbols with respect to their argument.
• The algorithm may be used algebraically, irrespective of the values of the parameters.
• It reproduces the exact results obtained by other authors in cases of especially simple parameters.