On some integrals involving the Hurwitz zeta function: part 2

Details On some integrals involving the Hurwitz zeta function: part 2 On some integrals involving the Hurwitz zeta function: part 2

2001-07-11

arxiv.org/abs/math/0107082v1

THE RAMANUJAN JOURNAL, 6, 449-468, 2002

Mathematics

Classical Analysis and ODEs

17 pages, AMS-LaTeX

Scientific paper

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.

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