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On some integrals involving the Hurwitz zeta function. II. (English) Zbl 1156.11333

Summary: 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 \(A_k(q) := k_{\zeta}\prime(1 - k, q)\), \(k \in \mathbb N\), and a family of polygamma functions of negative order, whose properties we study in some detail.
For Part I see Ramanujan J. 6, No. 2, 159–188 (2002; Zbl 1019.33001).

MSC:

11M35 Hurwitz and Lerch zeta functions
33E20 Other functions defined by series and integrals

Citations:

Zbl 1019.33001
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