Some approximations with 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 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 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 کاملSome Formulas for Apostol-euler Polynomials Associated with Hurwitz Zeta Function at Rational Arguments
Throughout this paper, we always make use of the following notation: N = {1, 2, 3, . . .} denotes the set of natural numbers, N0 = {0, 1, 2, 3, . . .} denotes the set of nonnegative integers, Z−0 = {0,−1,−2,−3, . . .} denotes the set of nonpositive integers, Z denotes the set of integers, R denotes the set of real numbers, C denotes the set of complex numbers. The generalized Bernoulli polynomi...
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ژورنال
عنوان ژورنال: Filomat
سال: 2020
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil2002528a