Results 81 to 90 of about 320 (178)
Some Relations of the Twisted q-Genocchi Numbers and Polynomials with Weight α and Weak Weight β
Abstract and Applied Analysis, 2012 Recently many mathematicians are working on Genocchi polynomials and Genocchi numbers. We define a new type of twisted q-Genocchi numbers and polynomials with weight 𝛼 and weak weight 𝛽 and give some interesting relations of the twisted q-Genocchi ...
J. Y. Kang, H. Y. Lee, N. S. Jung
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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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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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Some formulas related to Hurwitz–Lerch zeta functions [PDF]
The Ramanujan Journal, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Hurwitz Zeta Function as a Convergent Series
Rocky Mountain Journal of Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dwilewicz, Roman, Mináč, Ján
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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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Real zeros of Hurwitz–Lerch zeta and Hurwitz–Lerch type of Euler–Zagier double zeta functions [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2015 AbstractLet 0 < a ⩽ 1, s, z ∈ ${\mathbb{C}}$ and 0 < |z| ⩽ 1. Then the Hurwitz–Lerch zeta function is defined by Φ(s, a, z) ≔ ∑∞n = 0zn(n + a)− s when σ ≔ ℜ(s) > 1. In this paper, we show that the Hurwitz zeta function ζ(σ, a) ≔ Φ(σ, a, 1) does not vanish for all 0 < σ < 1 if and only if a ⩾ 1/2.
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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 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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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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