Integral representations of some series involving \({\binom {2k}k}^{-1} k^{-n}\) and some related series.

DOI10.1016/S0096-3003(02)00802-0zbMath1068.33003OpenAlexW1529137338MaRDI QIDQ1412632

Necdet Batir

Publication date: 25 November 2003

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00802-0

zbMATH Keywords

Riemann zeta functionPolylogarithmsSpecial functionsCatalan constantIntegral representationsLog-sine integrals

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Higher logarithm functions (33B30)

Related Items (9)

A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities ⋮ Massive Feynman diagrams and inverse binomial sums ⋮ On some series involving reciprocals of binomial coefficients ⋮ Series representations in the spirit of Ramanujan ⋮ Explicit evaluations of some families of log-sine and log-cosine integrals ⋮ Mahler measure and the WZ algorithm ⋮ On certain series involving reciprocals of binomial coefficients ⋮ Special values of the Riemann zeta function capture all real numbers ⋮ On the series \(\sum_{k=1}^\infty \binom {3k}{k}^{-1} k^{-n}x^k\)

Cites Work

• On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
• A class of series acceleration formulae for Catalan's constant
• Empirically Determined Apéry-Like Formulae for ζ(4n+3)
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