Gosper–type sums with reciprocals of binomial coefficients of the form (3n+ϵn)

DOI10.1080/10236198.2022.2138755zbMath1506.11034OpenAlexW4307566527MaRDI QIDQ5870242

Chu, Wenchang

Publication date: 6 January 2023

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2022.2138755

zbMATH Keywords

beta functionpolylogarithmintegral representationbinomial coefficientpartial fraction decompositionparametric integralGosper sums

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Gamma, beta and polygamma functions (33B15)

Cites Work

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• On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
• On the series \(\sum_{k=1}^\infty \binom {3k}{k}^{-1} k^{-n}x^k\)
• On some series involving reciprocals of binomial coefficients
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Surprising identities for the hypergeometric \({}_{4}F_{3}\) function
• Evaluations of binomial series
• An Explicit Evaluation of the Gosper Sum
• On certain series involving reciprocals of binomial coefficients
• Experimental Determination of Apéry-like Identities for ς(2n + 2)
• Interesting Series Involving the Central Binomial Coefficient
• INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS

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