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. Also, 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.

12 pages

References in corpus (1)

• The integral Mittag-Leffler, Whittaker and Wright functions

Cited by in corpus (1)

• Sums involving the digamma function connected to the incomplete beta function and the Bessel functions