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March 2016 Some results on Euler sums
Jinfa Cheng, Ce Xu
Funct. Approx. Comment. Math. 54(1): 25-37 (March 2016). DOI: 10.7169/facm/2016.54.1.3

Abstract

In the paper, we develop an approach to evaluation of Euler sums that involve harmonic numbers and alternating harmonic numbers. We give explicit formulae for several classes of Euler sums in terms of Riemann zeta values and prove that the quadratic sums ${S_{{l^2},l}}$ and cubic sums ${S_{{l^3},l}}$ reduce to linear sums and polynomials in zeta values. The approach is based on constructive Power series and Cauchy product computations.

Citation

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Jinfa Cheng. Ce Xu. "Some results on Euler sums." Funct. Approx. Comment. Math. 54 (1) 25 - 37, March 2016. https://doi.org/10.7169/facm/2016.54.1.3

Information

Published: March 2016
First available in Project Euclid: 22 March 2016

zbMATH: 06862332
MathSciNet: MR3477732
Digital Object Identifier: 10.7169/facm/2016.54.1.3

Subjects:
Primary: 11L99
Secondary: 11M06

Rights: Copyright © 2016 Adam Mickiewicz University

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Vol.54 • No. 1 • March 2016
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