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

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  • Robert Reynolds
  • Allan Stauffer
  • A. Ghareeb

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.

Suggested Citation

  • Robert Reynolds & Allan Stauffer & A. Ghareeb, 2022. "Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation," Journal of Mathematics, Hindawi, vol. 2022, pages 1-7, June.
    • Handle: RePEc:hin:jjmath:3591775
    DOI: 10.1155/2022/3591775
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