The evaluation of Tornheim double sums. Part2
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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.
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
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