Nonlinear Euler sums

István Mező

Vol. 272 (2014), No. 1, 201–226

DOI: 10.2140/pjm.2014.272.201

Abstract

We work out some formulas for nonlinear Euler sums involving multiple zeta values. As applications of these formulas, we give new closed form sums of several nonlinear Euler series, we present sums for powers of the digamma function and deduce the Landen identities for the polylogarithms by finite combinatorial identities.

Keywords

Euler sums, nonlinear Euler sums, polygamma functions, polylogarithm functions, Landen's identities, multiple zeta values

Mathematical Subject Classification 2010

Primary: 33B15, 11M32

Milestones

Received: 23 August 2013

Revised: 4 October 2013

Accepted: 8 October 2013

Published: 9 October 2014