On some explicit evaluations of nonlinear Euler sums

Abstract

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.