Results 91 to 100 of about 36,426 (206)
A discrete limit theorem for the periodic Hurwitz zeta-function
Lietuvos Matematikos Rinkinys, 2015 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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Further generalization of the extended Hurwitz-Lerch Zeta functions
Boletim da Sociedade Paranaense de Matemática, 2017 Recently various extensions of Hurwitz-Lerch Zeta functions have been investigated. Here, we first introduce a further generalization of the extended Hurwitz-Lerch Zeta functions. Then we investigate certain interesting and (potentially) useful properties, systematically, of the generalization of the extended Hurwitz-Lerch Zeta functions, for example ...
Rakesh K. Parmar +2 more
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The Zeta and Related Functions: Recent Developments
Journal of Advanced Engineering and Computation, 2019 The main object of this survey-cum-expository article is to present an overview of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a ...
H. M. Srivastava
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Derivatives of the Hurwitz Zeta function for rational arguments
Journal of Computational and Applied Mathematics, 1998 The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivatives of ζ(s,a) at negative odd s and rational a. For several of these rational arguments, closed-form expressions are given in terms of simpler transcendental functions, like the logarithm, the polygamma function, and the Riemann Zeta function.
Miller, Jeff, Adamchik, Victor S.
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Mean Value Properties of the Hurwitz Zeta-Function.
MATHEMATICA SCANDINAVICA, 1992 Let \(\zeta^* (s,x) = \zeta (s,x + 1)\), where \(\zeta (s,a)\) \((0 < a \leq 1)\) is the Hurwitz zeta-function. The author proves that \[ \int^ 1_ 0 \left | \zeta^* \Bigl( {1 \over 2} + it, x \Bigr) \right |^ 2 dx = \log \left( {t \over 2 \pi} \right) + \gamma - 2 \text{Re} {\zeta (1/2 + it) \over 1/2 + it} + O \left( {1 \over t} \right), \] where ...
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A Probabilistic Interpretation of the Hurwitz Zeta Function
Advances in Mathematics, 1993 Es sei \(\chi_ A\) die charakteristische Funktion einer Menge \(A\subset\mathbb{R}\). \textit{S. W. Golomb} [J. Number Theory 2, 189-192 (1970; Zbl 0198.381)] definierte bei beliebigem \(s>1\) auf \(\mathbb{N}\) das Wahrscheinlichkeitsmaß \[ Q_ s(A)={1\over {\zeta(s)}} \sum_{n=1}^ \infty \chi_ A(n)n^{-s} \qquad (A\subset\mathbb{N}).
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Differential Subordination Results for Certain Integrodifferential Operator and Its Applications
Abstract and Applied Analysis, 2012 We introduce an integrodifferential operator Js,b(f) which plays an important role in the Geometric Function Theory. Some theorems in differential subordination for Js,b(f) are used. Applications in Analytic Number Theory are also obtained which give new
M. A. Kutbi, A. A. Attiya
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A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks. [PDF]
Entropy (Basel), 2021 Jung H, Phoa FKH.
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Heavy Tails and the Shape of Modified Numerals. [PDF]
Cogn Sci, 2022 Carcassi F, Szymanik J.
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