Finite and Infinite Hypergeometric Sums Involving the Digamma Function

Juan Luis González-Santander and Fernando Sánchez Lasheras ()
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Juan Luis González-Santander: Department of Mathematics, University of Oviedo, C/ Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain
Fernando Sánchez Lasheras: Department of Mathematics, University of Oviedo, C/ Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain

Mathematics, 2022, vol. 10, issue 16, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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