Evaluation of Euler-Zagier sums
type: Item
instance of: scholarly article
title: Evaluation of Euler-Zagier sums
zbMATH Open document ID: 1015.11046
DOI: 10.1155/S016117120100521X
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-08-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50116
review text: A short and elegant evaluation of the triple sums \[ w(p,q,r):= \sum_{n,m=1}^{\infty} {1 \over n^p m^q (n+m)^r} \] in terms of single and double zeta values is given, where \(p>1\), \(r\geq 1\) are integers and \(q\geq 0\) is real with \(q+r>1\). The proof is based on a partial fraction identity and subsequent evaluation for the sum \(\sum_{n=1}^\infty {1 \over n^p (n+x)}\). This extends results going back to \textit{L. Tornheim} [Am. J. Math. 72, 303-314 (1950; Zbl 0036.17203)].
reviewed by: Roland Girgensohn
Mathematics Subject Classification ID: 11M99
Mathematics Subject Classification ID: 40B05
zbMATH DE Number: 1740560
zbMATH Keywords: Euler-Zagier sums
zbMATH Keywords: zeta function
zbMATH Keywords: polylogarithms
author: Khristo N. Boyadzhiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1740560