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Symmetry
Volume 17
Issue 7
10.3390/sym17071015
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Article

Further Formulae for Harmonic Series with Convergence Rate “-1/4”

by
Chunli Li
1 and
Wenchang Chu
2,*
1
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
2
Independent Researcher, Via Dalmazio Birago 9/E, 73100 Lecce, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(7), 1015; https://doi.org/10.3390/sym17071015 (registering DOI)
Submission received: 22 April 2025 / Revised: 19 June 2025 / Accepted: 20 June 2025 / Published: 27 June 2025
(This article belongs to the Special Issue Symmetry in Mathematical Theory and Simulation Methods for Backward Problems)
Review Reports Versions Notes

Abstract

By applying the “coefficient extraction method” to the symmetric transformation of hypergeometric series due to Chu and Zhang (2014), an overview is presented systematically for a large class of infinite series of convergence rate “−1/4” concerning harmonic numbers. Numerous closed formulae in terms of mathematical constants (such as π, ln2 and the Riemann zeta values) are established. They may serve as a reference source for readers in their further investigations.
Keywords: harmonic number; gamma function; central binomial coefficient; hypergeometric series; Riemann zeta function harmonic number; gamma function; central binomial coefficient; hypergeometric series; Riemann zeta function

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MDPI and ACS Style

Li, C.; Chu, W. Further Formulae for Harmonic Series with Convergence Rate “-1/4”. Symmetry 2025, 17, 1015. https://doi.org/10.3390/sym17071015

AMA Style

Li C, Chu W. Further Formulae for Harmonic Series with Convergence Rate “-1/4”. Symmetry. 2025; 17(7):1015. https://doi.org/10.3390/sym17071015

Chicago/Turabian Style

Li, Chunli, and Wenchang Chu. 2025. "Further Formulae for Harmonic Series with Convergence Rate “-1/4”" Symmetry 17, no. 7: 1015. https://doi.org/10.3390/sym17071015

APA Style

Li, C., & Chu, W. (2025). Further Formulae for Harmonic Series with Convergence Rate “-1/4”. Symmetry, 17(7), 1015. https://doi.org/10.3390/sym17071015

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