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Research Article | Open Access

Five classes of binomial/harmonic series of convergence rate − 1 / 4

Chunli Li1, 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 applying the "coefficient extraction method" to the symmetric transformation of hypergeometric series due to Chu and Zhang (2014), we examine systematically five classes of infinite series of convergence rate " − 1 / 4" containing binomial coefficients and harmonic numbers. Numerous closed formulae in terms of universal constants (such as π, ln ⁡ 2, and the Riemann zeta values) are established.

Keywords

hypergeometric seriesGamma functionharmonic numberRiemann zeta function
CLC number: Primary 11B65; Secondary 33C20, 65B10

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AIMS Mathematics
Volume 10 Issue 7,
July 2025
Pages 16264-16290
DOI: 10.3934/math.2025727

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Cite this article:
Li C, Chu W. Five classes of binomial/harmonic series of convergence rate − 1 / 4. AIMS Mathematics, 2025, 10(7): 16264-16290. https://doi.org/10.3934/math.2025727

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Received: 30 April 2025
Revised: 07 July 2025
Accepted: 15 July 2025
Published: 15 July 2025
©2025 the Author(s), licensee AIMS Press.

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