The evaluation of Tornheim double sums. Part2

dc.creatorEspinosa, Olivier
dc.creatorMoll, Victor H.
dc.date2008-11-04
dc.date.accessioned2026-07-07T10:15:26Z
dc.date.available2026-07-07T10:15:26Z
dc.descriptionWe provide an explicit formula for the Tornheim double series T(a,0,c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a=m, c=n, we show that in the most interesting case of even weight N:=m+n the Tornheim sum T(m,0,n) can be expressed in terms of zeta values and the family of integrals % \int_0^1 loggamma(q) B_{k}(q) Cl_{j+1} (2 πq) dq, % with k+j = N, where B_{k}(q) is a Bernoulli polynomial and \Cl_{j+1}(x) is a Clausen function.
dc.description38 pages, AMSLaTeX; submitted to Journal of Number Theory. "Tornheim.m", a Mathematica 6.0 package to work with Tornheim sums, is available for download from http://www.math.tulane.edu/~vhm/packages.html
dc.identifierhttps://arxiv.org/abs/0811.0557
dc.identifierhttp://arxiv.org/abs/0811.0557
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173175
dc.subjectNumber Theory
dc.subjectClassical Analysis and ODEs
dc.subject33E20; 11M35; 40C10
dc.titleThe evaluation of Tornheim double sums. Part2
dc.typetext

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