Some evaluation of harmonic number sums

DOI10.1080/10652469.2016.1231675zbMath1402.11114OpenAlexW2520413231MaRDI QIDQ5506810

Ce Xu, Weixia Zhu, Mingyu Zhang

Publication date: 16 December 2016

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2016.1231675

zbMATH Keywords

Riemann zeta functionpolylogarithm functionharmonic numberEuler sum

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Other Dirichlet series and zeta functions (11M41) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

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Cites Work

• Euler sums and integrals of polylogarithm functions
• Evaluation of the multiple zeta values \(\zeta(2,\ldots,2,3,2,\ldots,2)\)
• Nonlinear Euler sums
• Identities for the harmonic numbers and binomial coefficients
• The evaluation of character Euler double sums
• Quadratic alternating harmonic number sums
• Evaluations of some quadruple Euler sums of even weight
• 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