Results 181 to 190 of about 28,649 (209)

Two-sided inequalities for the extended Hurwitz–Lerch Zeta function

Computers and Mathematics With Applications, 2011
Recently, Srivastava et al. (2011) [2] unified and extended several interesting generalizations of the familiar Hurwitz–Lerch Zeta function Φ(z,s,a) by introducing a Fox–Wright type generalized hypergeometric function in the kernel.
H M Srivastava, Dragana Jankov, Tibor K Pogány   +2 more
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Integral transform of product of generalized k-Bessel function and generalized Hurwitz-Lerch Zeta function

Journal of Interdisciplinary Mathematics
The paper presents new integral formulae involving product of generalized K-Bessel function of first kind ωγ,α k,ϱ,b,c (z) and Hurwitz-Lerch Zeta (HLZ function) function ϕρ,σ ξ,η (z, s, d) are obtained and presented in terms of the generalized (Wright ...
Sanjay Sharma, N. Menaria
semanticscholar   +1 more source

On Statistical Properties of the Lerch Zeta‐Function

Lithuanian Mathematical Journal, 2001
The Lerch zeta-function with parameters \(01\) by the Dirichlet series \[ L(\lambda,\alpha,s)=\sum_{n=0}^\infty {\exp(2\pi i\lambda)\over (n+\alpha)^s}, \] and by analytic continuation elsewhere except for at most one simple pole at \(s=1\). Being a generalization of the famous Riemann zeta-function \(\zeta(s)=L(1,1,s)\), the value-distribution of the ...
openaire   +2 more sources

Convolution of values of the Lerch zeta-function

Journal of Number Theory, 2020
Motivated by the very classical ``convolutional'' result of the special depth 2 MZV \[\zeta(n-1,1)=\frac{n-1}{2} \zeta(n)-\frac{1}{2} \sum_{j=2}^{n-2} \zeta(j) \zeta(n-j),\] the authors prove a convolution identity for the Lerch zeta function \[\Phi(z ; \alpha ; s):=\sum_{n=0}^{\infty} \frac{z^{n}}{(n+\alpha)^{s}}.\] The main result is that, under ...
Murty, M. Ram, Pathak, Siddhi
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Applications of Hurwitz-Lerch Zeta Function to a Certain Class of Bi-Bazilevic and Pseudo-Starlike Functions

International Journal of Analysis and Applications
In this paper, we introduce a novel class of bi-univalent functions defined using the convolution of the normalized q-analogue of the Hurwitz–Lerch zeta function with the q-Srivastava–Attiya operator on the open unit disk D.
Waleed Al-Rawashdeh
semanticscholar   +1 more source

On universality of the Lerch zeta-function

Proceedings of the Steklov Institute of Mathematics, 2012
It is known that the Lerch zeta-function L(λ, α, s) with transcendental parameter α is universal in the Voronin sense; i.e., every analytic function can be approximated by shifts L(λ, α, s + iτ) uniformly on compact subsets of some region. In this paper, the universality for some classes of composite functions F(L(λ, α, s)) is obtained.
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The universality of the Lerch zeta-function

Lithuanian Mathematical Journal, 1997
Es sei \(0< \lambda< 1\), \(\alpha\) sei eine transzendente Zahl, und \(L(\lambda, \alpha,s)\) \((s\in \mathbb{C})\) bezeichne die Lerchsche Zetafunktion. Ferner sei \(D= \{s\in \mathbb{C}: \frac 12< \operatorname {Re}(s)< 1\}\), und \(\operatorname {mes}M\) sei das Lebesguemaß einer Lebesgue-meßbaren Menge \(M\subset \mathbb{R}\).
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The Hurwitz Zeta Function and the Lerch Zeta Function

2017
In this chapter we will discuss formulas we have developed for the evaluation of certain zeta functions. We will need them later for the numerical computation of the spectrum of the transfer operator. The implementations of these zeta functions are in a sense the heart of our computations, so we need to be very careful.
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On a certain set of Lerch’s zeta-functions and their derivatives∗

Lithuanian Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Statistical Properties of the Lerch Zeta-Function. II

Lithuanian Mathematical Journal, 2002
The Lerch zeta-function with parameters \(01\) by the Dirichlet series \[ L(\lambda,\alpha,s)=\sum_{n=0}^\infty {\exp(2\pi i\lambda)\over (n+\alpha)^s} \] and by analytic continuation elsewhere except for at most one simple pole at \(s=1\). In the present paper the author proves a discrete limit theorem for the Lerch zeta-function \(L(1,\alpha,s ...
openaire   +1 more source