The evaluation of Tornheim double sums. Part2
| dc.creator | Espinosa, Olivier | |
| dc.creator | Moll, Victor H. | |
| dc.date | 2008-11-04 | |
| dc.date.accessioned | 2026-07-07T10:15:26Z | |
| dc.date.available | 2026-07-07T10:15:26Z | |
| dc.description | We 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.description | 38 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.identifier | https://arxiv.org/abs/0811.0557 | |
| dc.identifier | http://arxiv.org/abs/0811.0557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173175 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33E20; 11M35; 40C10 | |
| dc.title | The evaluation of Tornheim double sums. Part2 | |
| dc.type | text |