Five classes of binomial/harmonic series of convergence rate $ -1/4 $

Chunli Li; Wenchang Chu; Chunli Li; Wenchang Chu

doi:10.3934/math.2025727

AIMS Mathematics

2025, Volume 10, Issue 7: 16264-16290. doi: 10.3934/math.2025727

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Five classes of binomial/harmonic series of convergence rate $ -1/4 $

Chunli Li ¹,
Wenchang Chu ^{2
,
,}

1.
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China
2.
Via Dalmazio Birago 9/E, Lecce 73100, Italy

Received: 30 April 2025 Revised: 07 July 2025 Accepted: 15 July 2025 Published: 18 July 2025
MSC : Primary 11B65; Secondary 33C20, 65B10

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 $ \pi $, $ \ln2 $, and the Riemann zeta values) are established.
- hypergeometric series,
- Gamma function,
- harmonic number,
- Riemann zeta function
Citation: Chunli Li, Wenchang Chu. Five classes of binomial/harmonic series of convergence rate $ -1/4 $[J]. AIMS Mathematics, 2025, 10(7): 16264-16290. doi: 10.3934/math.2025727

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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 $ \pi $, $ \ln2 $, and the Riemann zeta values) are established.

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