Research Article

A New Generalization of the Alternating Harmonic Series

Authors

  • ‪Jaafar ‬‏Alsayed Aleksandra 114-18, Riga LV-1011, Latvia

Abstract

Kilmer and Zheng (2021) recently introduced a generalized version of the alternating harmonic series. In this paper, we introduce a new generalization of the alternating harmonic series. A special case of our generalization converges to the Kilmer-Zheng series. Then we investigate several interesting and useful properties of this generalized, such as a summation formula related to the Hurwitz -Lerch Zeta function, a duplication formula, an integral representation, derivatives, and the recurrence relationship. Some important special cases of the main results are also discussed.

Article information

Journal

Journal of Mathematics and Statistics Studies

Volume (Issue)

4 (4)

Pages

70-75

Published

2023-11-04

How to Cite

A New Generalization of the Alternating Harmonic Series. (2023). Journal of Mathematics and Statistics Studies, 4(4), 70-75. https://doi.org/10.32996/jmss.2023.4.4.7

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Views

23

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8

Keywords:

Alternating Harmonic Series, Dirichlet eta function, Hurwitz -Lerch Zeta function, Polylogarithm function

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