On some series involving reciprocals of binomial coefficients

DOI10.1016/j.amc.2013.05.053zbMath1329.40001OpenAlexW2007938209MaRDI QIDQ902512

Anthony Sofo, Necdet Batir

Publication date: 18 January 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.05.053

zbMATH Keywords

combinatorial identitiesintegral representationsseriesbinomial coefficientsCatalan constantApéry constantreciprocal binomial sums

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Convergence and divergence of infinite limiting processes (40Axx)

Related Items (2)

Combinatorial identities involving reciprocals of the binomial and central binomial coefficients and harmonic numbers ⋮ Gosper–type sums with reciprocals of binomial coefficients of the form (3n+ϵn)

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 \(\sum_{k=1}^\infty \binom {3k}{k}^{-1} k^{-n}x^k\)
• Massive Feynman diagrams and inverse binomial sums
• Integral representations of some series involving \({\binom {2k}k}^{-1} k^{-n}\) and some related series.
• Values of the Riemann zeta functions and integrals involving \(\log (2\sinh {\theta\over 2})\) and \(\log (2\sin {\theta\over 2})\)
• Evaluations of binomial series
• On certain series involving reciprocals of binomial coefficients
• Experimental Determination of Apéry-like Identities for ς(2n + 2)
• Mahler measure and the WZ algorithm

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