Evaluation of Apéry-like series through multisection method

DOI10.7153/jca-2018-12-06zbMath1424.11175OpenAlexW2884423540MaRDI QIDQ4627857

Chu, Wenchang, Flavia Esposito

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jca-2018-12-06

zbMATH Keywords

central binomial coefficientApéry-like seriesmultisection series

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Evaluation of number-theoretic constants (11Y60)

Related Items

Alternating series of Apéry-type for the Riemann zeta function.

Cites Work

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• On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
• Multisection method and further formulae for \(\pi\)
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• The quest for pi
• Some binomial series obtained by the WZ-method
• Hypergeometric identities for 10 extended Ramanujan-type series
• Evaluations of binomial series
• Some interesting series arising from the power series expansion of \((\sin^{-1}x)^q\)
• Central Binomial Sums, Multiple Clausen Values, and Zeta Values
• Binomial sums involving harmonic numbers
• Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
• Ramanujan's Series for 1/π: A Survey
• Interesting Series Involving the Central Binomial Coefficient
• Hypergeometric series and the Riemann zeta function
• Some New Formulas for π
• INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS
• A Generalized Apery Series
• Symmetric functions and the Riemann zeta series