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INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS

Part of: Acceleration of convergence Zeta and $L$-functions: analytic theory Sequences and sets

Published online by Cambridge University Press:  07 July 2023

CHUNLI LI Open the ORCID record for CHUNLI LI [Opens in a new window]  and
WENCHANG CHU Open the ORCID record for WENCHANG CHU [Opens in a new window]
CHUNLI LI
Affiliation:
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), PR China e-mail: lichunlizk@outlook.com
WENCHANG CHU*
Affiliation:
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), PR China
*
e-mail: hypergeometricx@outlook.com
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Abstract

By examining two hypergeometric series transformations, we establish several remarkable infinite series identities involving harmonic numbers and quintic central binomial coefficients, including five conjectured recently by Z.-W. Sun [‘Series with summands involving harmonic numbers’, Preprint, 2023, arXiv:2210.07238v7]. This is realised by ‘the coefficient extraction method’ implemented by Mathematica commands.

Keywords

Riemann zeta functionharmonic numbercentral binomial coefficient

MSC classification

Primary: 11B65: Binomial coefficients; factorials; $q$-identities
Secondary: 11M06: $zeta (s)$ and $L(s, chi)$ 65B10: Summation of series
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 2 , April 2024 , pp. 225 - 241
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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