Results 1 to 10 of about 7,133 (231)
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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On the Hurwitz zeta function with an application to the beta-exponential distribution [PDF]
Journal of Inequalities and Applications, 2020 We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders.
Julyan Arbel +2 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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Analytic continuation of the Hurwitz Zeta Function with physical application [PDF]
, 2002 A new formula relating the analytic continuation of the Hurwitz zeta function to the Euler gamma function and a polylogarithmic function is presented. In particular, the values of the first derivative of the real part of the analytic continuation of the ...
Beneventano C. G. +7 more
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Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function [PDF]
Abstract and Applied Analysis, 2013 By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch zeta function as well as a new expansion formula for ...
S. Gaboury, A. Bayad
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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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Zeros of the Hurwitz zeta function in the interval (0,1) [PDF]
, 2011 We first give a condition on the parameters $s,w$ under which the Hurwitz zeta function $\zeta(s,w)$ has no zeros and is actually negative. As a corollary we derive that it is nonzero for $w\geq 1$ and $s\in(0,1)$ and, as a particular instance, the known
Schipani, Davide
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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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Further extension of the generalized Hurwitz-Lerch Zeta function of two variables [PDF]
, 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
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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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