On alternating analogues of Tornheim's double series. II
type: Item
instance of: scholarly article
title: On alternating analogues of Tornheim's double series. II
zbMATH Open document ID: 1192.11059
author: Hirofumi Tsumura
published in: The Ramanujan Journal
publication date: 2009-11-23T00:00:00Z
review text: Let \[ R(p,q,r)=\sum_{m,n=1}^\infty\frac{(-1)^n}{m^pn^q(m+n)^r}, \] \[ \mathfrak{T}_{b_1,b_2}(p,q,r)=\sum_{m,n=0}^\infty 1/{(2m+b_1)^p(2n+b_2)^q(2m+2n+b_1+b_2)^r}, \] where \(b_1,b_2\in\{1,2\}\). The author proves: Theorem. Suppose \(k,l,d\in\mathbb{N}\) with \(d\geq 2\) and \(k+l+d\equiv 1 \pmod 2\). Then \(R(k,l,d)\) and \(\mathfrak{T}_{b_1,b_2}(k,l,d)\) can be expressed as polynomials in \(\{\zeta(j)\mid 2\leq j\leq k+l+d\}\) with rational coefficients, where \(\zeta(s)\) is Riemann's zeta function. Part I, see Proc. Am. Math. Soc. 131, No. 12, 3633--3641 (2003; Zbl 1045.11057).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 40B05
zbMATH DE Number: 5636931
zbMATH Keywords: Tornheim double series
MaRDI profile type: Publication
full work available at URL: s11139-007-9016-x
OpenAlex ID: W2058239821
cites work: Zeros of Bernoulli, generalized Bernoulli and Euler polynomials
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cites work: Evaluation formulas for Tornheim’s type of alternating double series
DOI: 10.1007/S11139-007-9016-X
description: scientific article; zbMATH DE number 5636931