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Research Article | Open Access

Alternating series in terms of Riemann zeta function and Dirichlet beta function

Zhiling Fan1, Wenchang Chu2( )
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China
Via Dalmazio Birago 9/E, Lecce 73100, Italy
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Abstract

By making use of the multisection series method, four classes of alternating infinite series are evaluated, in closed form, by the Riemann zeta function and the Dirichlet beta function.

Keywords

infinite summationhigher derivativeinteger functionRiemann zeta functionDirichlet beta function

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Electronic Research Archive
Volume 32 Issue 2,
February 2024
Pages 1227-1238
DOI: 10.3934/era.2024058

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Cite this article:
Fan Z, Chu W. Alternating series in terms of Riemann zeta function and Dirichlet beta function. Electronic Research Archive, 2024, 32(2): 1227-1238. https://doi.org/10.3934/era.2024058

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Received: 19 September 2023
Revised: 15 January 2024
Accepted: 25 January 2024
Published: 30 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)