Generalization of the Flajolet Salvy identities for Euler Sums

Linear Euler harmonic sums

Abstract

The exploration of linear Euler harmonic sums had its beginnings with the works of Euler in the 18th century. In 1998 Flajolet and Salvy published a seminal paper in which they developed an approach to the evaluation of linear Euler harmonic sums and gave explicit formulae for several classes of Euler sums in terms of Riemann zeta and other special function values. In this paper, results given by Flajolet and Salvy are extended and generalized.