On some slowly convergent series involving the Hurwitz zeta-function
نویسندگان
چکیده
منابع مشابه
On Some Definite Integrals Involving the Hurwitz Zeta Function
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).
متن کاملOn Some Integrals Involving the Hurwitz Zeta Function: Part 2
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(πq), ln (q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak (q) := kζ ′(1−k, q), k ∈ N, and a family of polygamma functions of negative ...
متن کاملOn Some Integrals Involving the Hurwitz Zeta
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).
متن کاملOn Some Integrals Involving the Hurwitz Zeta Function: Part 2
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(πq), ln Γ(q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak(q) := kζ (1 − k, q), k ∈ N, and a family of polygamma functions o...
متن کاملHypergeometric Series Associated with the Hurwitz-lerch Zeta Function
The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations, differential relations, series expansion and discuss the link with known results.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(03)00617-4