Quadratic and cubic harmonic number sums

DOI10.1016/j.jmaa.2016.10.026zbMath1349.11053OpenAlexW2537491657MaRDI QIDQ335433

Mingyu Zhang, Ce Xu, Xin Si

Publication date: 2 November 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.10.026

zbMATH Keywords

Riemann zeta functionEuler sumsharmonic numberspolylogarithm function

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) (zeta (s)) and (L(s, chi)) (11M06) Other combinatorial number theory (11B75) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (16)

Some evaluations of parametric Euler type sums of harmonic numbers ⋮ On harmonic numbers and nonlinear Euler sums ⋮ Extension of the four Euler sums being linear with parameters and series involving the zeta functions ⋮ Euler sums and Stirling sums ⋮ Generalized harmonic number sums and quasisymmetric functions ⋮ Unnamed Item ⋮ Gauss's theorem and harmonic number summation formulae with certain mathematical constants ⋮ Unnamed Item ⋮ Alternating cubic Euler sums with binomial squared terms ⋮ General order Euler sums with multiple argument ⋮ Watson-type₃F₂-series and summation formulae involving generalized harmonic numbers ⋮ Four parametric linear Euler sums ⋮ Unnamed Item ⋮ Some evaluations of infinite series involving parametric harmonic numbers ⋮ Evaluations of sums involving harmonic numbers and binomial coefficients ⋮ Identities for the shifted harmonic numbers and binomial coeffecients

Cites Work

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• Euler sums and integrals of polylogarithm functions
• Nonlinear Euler sums
• Identities for the harmonic numbers and binomial coefficients
• The evaluation of character Euler double sums
• Double Euler sums on Hurwitz zeta functions
• Quadratic alternating harmonic number sums
• Evaluations of some quadruple Euler sums of even weight
• Making sense of experimental mathematics
• Harmonic sums and integral representations
• Euler Sums and Contour Integral Representations
• Experimental Evaluation of Euler Sums
• Special values of multiple polylogarithms
• Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
• Explicit evaluation of Euler sums
• Computation and theory of extended Mordell-Tornheim-Witten sums
• SHIFTED HARMONIC SUMS OF ORDER TWO

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