Finite and Infinite Hypergeometric Sums Involving the Digamma Function

Abstract

We calculate some finite and infinite sums containing the digamma function in closed form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative formulas of the Pochhammer symbol. Additionally, we compare two different differentiation formulas of the generalized hypergeometric function with respect to the parameters. For some particular cases, we recover some results found in the literature. Finally, all the results have been numerically checked.

Keywords

• digamma function
• differentiation with respect to parameters
• closed-form sums calculation