Integral forms of sums associated with harmonic numbers

DOI10.1016/j.amc.2008.10.044zbMath1175.11007OpenAlexW2004318253MaRDI QIDQ1002291

Anthony Sofo

Publication date: 25 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.10.044

zbMATH Keywords

identitiesintegral representationsbinomial coefficientsharmonic numbers

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65)

Related Items (28)

Harmonic number identities via hypergeometric series and Bell polynomials ⋮ Identities for alternating inverse squared binomial and harmonic number sums ⋮ Identities for Reciprocal Binomials ⋮ Ramanujan formula for the generalized Stirling approximation ⋮ Riordan arrays and harmonic number identities ⋮ Estimating the digamma and trigamma functions by completely monotonicity arguments ⋮ Identities on harmonic and \(q\)-harmonic number sums ⋮ Sums of quadratic half integer harmonic numbers of alternating type ⋮ Half-integer values of the sums of harmonic numbers of order two ⋮ Harmonic numbers and cubed binomial coefficients ⋮ New families of alternating harmonic number sums ⋮ Alternating cubic Euler sums with binomial squared terms ⋮ Mixed binomial sum identities ⋮ Harmonic number identities via the Newton-Andrews method ⋮ Identities for the harmonic numbers and binomial coefficients ⋮ Summation formula involving harmonic numbers ⋮ Unnamed Item ⋮ On generalized harmonic number sums ⋮ New improvements of the Stirling formula ⋮ Explicit evaluation of harmonic sums ⋮ Unnamed Item ⋮ Harmonic numbers at half integer values ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Harmonic numbers and double binomial coefficients ⋮ Quadratic alternating harmonic number sums ⋮ Harmonic sums and integral representations ⋮ Identities for the shifted harmonic numbers and binomial coeffecients

Cites Work

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• Mellin transforms and asymptotics: Finite differences and Rice's integrals
• On Stirling numbers and Euler sums
• Hypergeometric series and harmonic number identities
• Some more identities involving rational sums
• Some Identities Involving Harmonic Numbers
• The Method of Coefficients

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