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Volume 14
Issue 11
10.3390/axioms14110776
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients

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.
Axioms 2025, 14(11), 776; https://doi.org/10.3390/axioms14110776
Submission received: 9 September 2025 / Revised: 11 October 2025 / Accepted: 21 October 2025 / Published: 23 October 2025
(This article belongs to the Special Issue Special Functions and Related Topics, 2nd Edition)
Versions Notes

Abstract

We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is systematically investigated. Numerous closed summation formulae are established, including a remarkable series about harmonic numbers of the third order.
Keywords: harmonic number; central binomial coefficient; hypergeometric series harmonic number; central binomial coefficient; hypergeometric series

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MDPI and ACS Style

Li, C.; Chu, W. Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients. Axioms 2025, 14, 776. https://doi.org/10.3390/axioms14110776

AMA Style

Li C, Chu W. Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients. Axioms. 2025; 14(11):776. https://doi.org/10.3390/axioms14110776

Chicago/Turabian Style

Li, Chunli, and Wenchang Chu. 2025. "Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients" Axioms 14, no. 11: 776. https://doi.org/10.3390/axioms14110776

APA Style

Li, C., & Chu, W. (2025). Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients. Axioms, 14(11), 776. https://doi.org/10.3390/axioms14110776

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