Results 1 to 10 of about 220 (22)

A symbolic approach to multiple Hurwitz zeta values at non-positive integers

Open Mathematics, 2023
In this article, we give another method to calculate the values of multiple Hurwitz zeta function at non-positive integers by means of Raabe’s formula and the Bernoulli numbers and we simplify these values by symbolic computation techniques.
Sadaoui Boualem, Jarad Fahd, Adjabi Yacine, Türkan Erkan Murat   +3 more
doaj   +1 more source

Fractional calculus, zeta functions and Shannon entropy

Open Mathematics, 2021
This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ\zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative.
Guariglia Emanuel
doaj   +1 more source

Vanishing of the integral of the Hurwitz zeta function [PDF]

, 2002
A proof is given that the improper Riemann integral of δ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with R(s) < 1.
Broughan, Kevin A.
core   +2 more sources

Remarks on the mixed joint universality for a class of zeta-functions

, 2016
Two remarks related with the mixed joint universality for a polynomial Euler product and a periodic Hurwitz zeta-function with a transcendental parameter are given.
Hilbert, Javtokas, Kačinskaitė, KOHJI MATSUMOTO, Laurinčikas, Laurinčikas, Laurinčikas, Matsumoto, ROMA KAČINSKAITĖ, Steuding, Voronin   +10 more
core   +1 more source

Further extension of the generalized Hurwitz-Lerch Zeta function of two variables

, 2019
The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with generalized ...
Nisar, Kottakkaran Sooppy
core   +1 more source

q-Analogues of the Barnes multiple zeta functions

, 2004
In this paper, we introduce $q$-analogues of the Barnes multiple zeta functions. We show that these functions can be extended meromorphically to the whole plane, and moreover, tend to the Barnes multiple zeta functions when $q\uparrow 1$ for all complex ...
Yamasaki, Yoshinori
core   +2 more sources

Joint approximation of analytic functions by the shifts of Hurwitz zeta-functions in short intervals

Open Mathematics
In the article, we obtain that, for algebraically independent over Q{\mathbb{Q}} parameters α1,…,αr{\alpha }_{1},\ldots ,{\alpha }_{r}, there are infinitely many shifts (ζ(s+iτ,α1),…,ζ(s+iτ,αr))\left(\zeta \left(s+i\tau ,{\alpha }_{1}),\ldots ,\zeta ...
Laurinčikas Antanas, Šiaučiūnas Darius   +1 more
doaj   +1 more source

Double series expression for the Stieltjes constants

, 2011
We present expressions in terms of a double infinite series for the Stieltjes constants $\gamma_k(a)$. These constants appear in the regular part of the Laurent expansion for the Hurwitz zeta function.
Coffey, Mark W.
core   +1 more source

Integral representations of q-analogues of the Hurwitz zeta function

, 2005
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of ...
DM Bradley, ET Whittaker, GE Andrews, H Tsumura, H Tsumura, J Satoh, M Kaneko, Masato Wakayama, N Koblitz, N Kurokawa, P Appell, Y Hashimoto, Yoshinori Yamasaki   +12 more
core   +1 more source

On hypergeometric Bernoulli numbers and polynomials [PDF]

, 2015
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.Comment: 12 ...
Hu, Su, Kim, Min-Soo
core