On some integrals involving the Hurwitz zeta function: part 2
经典分析与常微分方程
2008-11-07 v1 数学物理
math.MP
摘要
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.
引用
@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}
}
备注
17 pages, AMS-LaTeX