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arXiv · 0811.0557

The evaluation of Tornheim double sums. Part2

Olivier Espinosa·Victor H. Moll
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Abstract

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.

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Olivier Espinosa, Victor H. Moll. 2008-11-04. The evaluation of Tornheim double sums. Part2. https://arxiv.org/abs/0811.0557

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