Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation

Robert Reynolds, Allan Stauffer and A. Ghareeb

Journal of Mathematics, 2022, vol. 2022, 1-7

Abstract: We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions. A new recurrence identity with consecutive neighbours and the product of trigonometric functions is derived.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3591775

DOI: 10.1155/2022/3591775

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