Evaluations of nonlinear Euler sums of weight ten

Ce Xu

Applied Mathematics and Computation, 2019, vol. 346, issue C, 594-611

Abstract: In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all quadratic Euler sums of weight ten. Furthermore, we also establish some relations between multiple zeta (star) values and nonlinear Euler sums. As applications of these relations, we give new closed form representations of several cubic Euler sums through single zeta values and linear sums. Finally, with the help of numerical computations of Mathematica or Maple, we evaluate several other Euler sums of weight ten.

Keywords: Harmonic number; polylogarithm function; Euler sum; Riemann zeta function; Multiple zeta (star) value; Multiple harmonic (star) sum (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:594-611

DOI: 10.1016/j.amc.2018.10.042

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