Euler Sums and Contour Integral Representations

Philippe Flajolet (1) , Bruno Salvy (1)

1 ALGO - Algorithms

This paper develops an approach to the evaluation of Euler sums involving harmonic numbers either linearly or nonlinearly. We give explicit formul{æ} for certain classes of Euler sums in terms of values of the Riemann zeta function at positive integers. The approach is based on simple contour integral representations and residue computations.

Domaines: Autre [cs.OH]

Philippe Flajolet, Bruno Salvy. Euler Sums and Contour Integral Representations. [Research Report] RR-2917, INRIA. 1996. ⟨inria-00073780⟩