INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS

DOI10.1017/s0004972723000618OpenAlexW4383552621MaRDI QIDQ6124021

Chu, Wenchang, Chun-li Li

Publication date: 9 April 2024

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972723000618

zbMATH Keywords

Riemann zeta functionharmonic numbercentral binomial coefficient

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06) Numerical summation of series (65B10)

Cites Work

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• On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
• Infinite series identities derived from the very well-poised \(\Omega\)-sum
• Generators of some Ramanujan formulas
• Dixon's \(_3F_2(1)\)-series and identities involving harmonic numbers and the Riemann zeta function
• Cubic modular equations and new Ramanujan-type series for \(1/\pi\).
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• Further Apéry-like series for Riemann zeta function
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• Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
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• Interesting Series Involving the Central Binomial Coefficient
• Hypergeometric series and the Riemann zeta function
• About a New Kind of Ramanujan-Type Series
• Hypergeometric approach to Apéry-like series

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