Evaluations of binomial series

DOI10.1007/s00010-005-2774-xzbMath1078.05003OpenAlexW2091771439WikidataQ56935700 ScholiaQ56935700MaRDI QIDQ2567989

Roland Girgensohn, Jonathan M. Borwein

Publication date: 6 October 2005

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-005-2774-x

zbMATH Keywords

polylogarithmsbinomial coefficientsinteger relation algorithms

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Number-theoretic algorithms; complexity (11Y16)

Related Items (14)

Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS ⋮ From Madhava–Leibniz to Lehmer’s Limit ⋮ REMARKABLE RELATIONS BETWEEN THE CENTRAL BINOMIAL SERIES, EULERIAN POLYNOMIALS, AND POLY-BERNOULLI NUMBERS, LEADING TO STEPHAN'S OBSERVATION ⋮ On some series involving reciprocals of binomial coefficients ⋮ Rational combinations for the sums involving inverse binomial coefficients ⋮ Evaluation of Apéry-like series through multisection method ⋮ Some Double Sums Involving Ratios of Binomial Coefficients Arising From Urn Models ⋮ FINITE SUMS CONNECTED WITH THE INVERSES OF CENTRAL BINOMIAL NUMBERS AND CATALAN NUMBERS ⋮ Combinatorial properties of poly-Bernoulli relatives ⋮ On certain series involving reciprocals of binomial coefficients ⋮ Unnamed Item ⋮ Gosper–type sums with reciprocals of binomial coefficients of the form (3n+ϵn) ⋮ On the series \(\sum_{k=1}^\infty \binom {3k}{k}^{-1} k^{-n}x^k\)

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