Vol. 272, No. 1, 2014

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Nonlinear Euler sums

István Mező

Vol. 272 (2014), No. 1, 201–226
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
Authors
István Mező
Department of Mathematics
Nanjing University of Information Science and Technology
Nanjing, 210044
China