On some explicit evaluations of nonlinear Euler sums

  • Jichao Zhang
  • Ce XuEmail author


In this paper, we extend tools developed in [26] to study harmonic numbers sums. We use these objects to compute Euler-related sums and to explore their connections with classical Euler sums. We establish some new relations between Euler sums and related sums. The relations obtained allow us to find some nice closed-form representations of nonlinear Euler sums through zeta values and linear sums.


Euler sums Tornheim type series harmonic numbers Riemann zeta function 


40A05 33B99 33E20 11M06 11M32 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceHubei University of TechnologyWuhanChina
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenChina

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