# The evaluation of Tornheim double sums. Part 1

Research paper by Olivier Espinosa, Victor H. Moll

Indexed on: 30 May '05Published on: 30 May '05Published in: Mathematics - Classical Analysis and ODEs

#### Abstract

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 $A_k (q): = k\zeta '(1 - k,q)$.