The evaluation of Tornheim double sums. Part 1

Details The evaluation of Tornheim double sums. Part 1 The evaluation of Tornheim double sums. Part 1

2005-05-30

arxiv.org/abs/math/0505647v1

Journal of Number Theory, 116 (2006) 200 - 229

Mathematics

Classical Analysis and ODEs

23 pages, AMS-LaTex, to appear in Journal of Number Theory

Scientific paper

We provide an explicit formula for the Tornheim double series in terms of integrals involving the Hurwitz zeta function. We also study the limit when the parameters of the Tornheim sum become natural numbers, and show that in that case it can be expressed in terms of definite integrals of triple products of Bernoulli polynomials and the Bernoulli function $A_k (q): = k\zeta '(1 - k,q)$.

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