  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 (\pi q), ln Gamma(q) and the polygamma
functions. Many of the results are most conveniently formulated in terms of a
family of functions A_k(q):=k zeta'(1-k,q), where k is a natural number, and a
family of polygamma functions of negative order, whose properties we study in
some detail.
