Results 11 to 20 of about 7,129 (230)
Hurwitz Zeta Function Is Prime
Mathematics, 2023 We proved that the Hurwitz zeta function is prime. In addition, we derived the Nevanlinna characteristic for this function.
Marius Dundulis +3 more
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A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function [PDF]
Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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Analytical properties of the Hurwitz–Lerch zeta function [PDF]
Advances in Difference Equations, 2020 In the present paper, we aim to extend the Hurwitz–Lerch zeta function Φ δ , ς ; γ ( ξ , s , υ ; p ) $\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)$ involving the extension of the beta function (Choi et al. in Honam Math. J.
Raghib Nadeem +3 more
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On the Hurwitz Zeta Function [PDF]
, 2011 We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.
Lazhar Fekih‐Ahmed
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A discrete limit theorem for the periodic Hurwitz zeta-function. II
Lietuvos Matematikos Rinkinys, 2016 In the paper, we prove a limit theorem of discrete type on the weak convergence of probability measures on the complex plane for the periodic Hurwitz zeta-function.
Audronė Rimkevičienė
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JOINT UNIVERSALITY OF HURWITZ ZETA-FUNCTIONS [PDF]
Bulletin of the Australian Mathematical Society, 2012 AbstractIt is well known that Hurwitz zeta-functions with algebraically independent parameters over the field of rational numbers are universal in the sense that their shifts approximate simultaneously any collection of analytic functions. In this paper we introduce some classes of universal composite functions of a collection of Hurwitz zeta-functions.
ANTANAS LAURINČIKAS
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AIMS Mathematics, 2022 A Prudnikov sum is extended to derive the finite sum of the Hurwitz-Lerch Zeta function in terms of the Hurwitz-Lerch Zeta function. This formula is then used to evaluate a number trigonometric sums and products in terms of other trigonometric functions.
Robert Reynolds, Allan Stauffer
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On the Mishou Theorem for Zeta-Functions with Periodic Coefficients
Mathematics, 2023 Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet ...
Aidas Balčiūnas +3 more
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LINEAR COMBINATIONS OF HURWITZ ZETA-FUNCTIONS
Kyushu Journal of Mathematics, 2022 As it is well known, the Hurwitz zeta-function, for \(\sigma>1\) and a parameter \(\alpha ...
Steuding, Rasa, Steuding, Jörn
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Hyperharmonic series involving Hurwitz zeta function
Journal of Number Theory, 2009 For integers \(r\geq 1\) and \(m\geq r+1\) the authors prove that \[ \sum_{n=1}^\infty\frac{H_n^{(r)}}{n^m}=\sum_{n=1}^\infty H_n^{(r-1)}\sum_{p=0}^\infty\frac{1}{(n+p)^m}, \] where \(H_n^{(r)}\) are the hyperharmonic numbers.
István Mező, Ayhan Dil
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