New series involving harmonic numbers and squared central binomial coefficients

DOI10.1216/RMJ-2019-49-8-2513zbMath1434.33028OpenAlexW3003433048MaRDI QIDQ2293661

John Maxwell Campbell

Publication date: 5 February 2020

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1580461779

zbMATH Keywords

harmonic numbercentral binomial coefficientseries with harmonic numbers

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other functions defined by series and integrals (33E20)

Related Items (16)

Applications of Zeilberger’s Algorithm to Ramanujan-Inspired Series Involving Harmonic-Type Numbers ⋮ Convolution identities involving the central binomial coefficients and Catalan numbers ⋮ Explicit identities for infinite families of series involving squared binomial coefficients ⋮ A natural companion to Catalan's constant ⋮ Infinite series involving harmonic numbers of convergence rate 1/2 ⋮ Identities for Catalan's constant arising from integrals depending on a parameter ⋮ Series containing squared central binomial coefficients and alternating harmonic numbers ⋮ Unnamed Item ⋮ Two integrals involving the Legendre chi function ⋮ Unnamed Item ⋮ On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums ⋮ Unnamed Item ⋮ Harmonic sums from the Kummer theorem ⋮ Lemniscate-like constants and infinite series ⋮ Series with harmonic-like numbers and squared binomial coefficients ⋮ Symbolic computations via Fourier–Legendre expansions and fractional operators

Cites Work

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• More hypergeometric identities related to Ramanujan-type series
• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• Integer powers of arcsin
• Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers
• Congruences for central binomial sums and finite polylogarithms
• \(p\)-adic congruences motivated by series
• A new series for π³and related congruences
• New series for some special values of $L$-functions
• Binomial sums involving harmonic numbers
• The lemniscate constants
• Generalized harmonic number summation formulae via hypergeometric series and digamma functions
• Supercongruences related to 3F2(1) involving harmonic numbers
• An integral transform related to series involving alternating harmonic numbers
• INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS
• RANDOM WALKS, ELLIPTIC INTEGRALS AND RELATED CONSTANTS

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