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