Abstract. We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(πq), ln Γ(q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak(q) := kζ (1 − k, q), k ∈ N, and a family of polygamma functions o...

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 Ak(q) := kζ(1− k, q).