Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients

DOI10.1007/s11139-019-00140-5zbMath1444.33005OpenAlexW2947309445MaRDI QIDQ780450

Chu, Wenchang, Xiao Yuan Wang

Publication date: 15 July 2020

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-019-00140-5

zbMATH Keywords

hypergeometric seriesGamma functionharmonic numberscentral binomial coefficientRamanujan-like seriesGauss summation theorem

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Numerical summation of series (65B10)

Related Items (19)

Applications of Zeilberger’s Algorithm to Ramanujan-Inspired Series Involving Harmonic-Type Numbers ⋮ Explicit identities for infinite families of series involving squared binomial coefficients ⋮ A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications ⋮ A natural companion to Catalan's constant ⋮ Infinite series involving harmonic numbers of convergence rate 1/2 ⋮ Infinite series around multinomial coefficients and harmonic numbers ⋮ INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS ⋮ On a problem involving the squares of odd harmonic numbers ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ Infinite series on quadratic skew harmonic numbers ⋮ Expansions over Legendre polynomials and infinite double series identities ⋮ Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera ⋮ Unnamed Item ⋮ Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Harmonic sums from the Kummer theorem ⋮ Lemniscate-like constants and infinite series ⋮ Series with harmonic-like numbers and squared binomial coefficients

Uses Software

• OEIS

Cites Work

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• Hypergeometric approach to Weideman's conjecture
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• Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters
• Interesting Series Involving the Central Binomial Coefficient
• Hypergeometric series and the Riemann zeta function
• Generalized harmonic number summation formulae via hypergeometric series and digamma functions
• Hypergeometric approach to Apéry-like series

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