On some integrals involving the Hurwitz zeta function: part 2
Classical Analysis and ODEs
2008-11-07 v1 Mathematical Physics
math.MP
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 (\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.
Cite
@article{arxiv.math/0107082,
title = {On some integrals involving the Hurwitz zeta function: part 2},
author = {Olivier R. Espinosa and Victor H. Moll},
journal= {arXiv preprint arXiv:math/0107082},
year = {2008}
}
Comments
17 pages, AMS-LaTeX