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

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.

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Publication Details

Journal
Symmetry
Published
2025-06-27
DOI
https://doi.org/10.3390/sym17071015
Primary Topic
Differential Equations and Boundary Problems
Type
article
Field-Weighted Citation Impact
0.00
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article

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

Wenchang Chu, Chunli Li
Symmetry
Differential Equations and Boundary Problems
article

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

Wenchang Chu, Chunli Li
article en

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.

SymmetryVol. 17(7)
Zhoukou Normal University (CN)
Openalex Percentile: Top 77%
Differential Equations and Boundary Problems
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Further Formulae for Harmonic Series with Convergence Rate “−1/4” — Wenchang Chu, Chunli Li · Symmetry (2025) | TGRS Research Map | TGRS