Results 171 to 180 of about 26,951 (214)

Approximation of the Lerch Zeta-Function

Lithuanian Mathematical Journal, 2004
For \(\sigma > 1\), with real parameters \(\lambda\) and \(\alpha\), \(0 < \alpha \leq 1\), the Lerch zeta--function is defined by \[ L(\lambda, \alpha, s) = \sum_{m=0}^\infty {{e^{2\pi i \lambda m}} \over {(m+\alpha)^s}}, \] and can be continued analytically. Improving on an approximation in the monograph by the author and A.
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A Study on Analytic Functions Associated with the Generalized Hurwitz-Lerch zeta Function

University of Zawia Journal of Natural Sciences
In this study, we introduce and investigate new subclasses of analytic functions that are closely related to the generalized Hurwitz-Lerch zeta function.
A. A. Abubaker
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Inclusion and Subordination Features of a Particular Subclass of p -Valent Meromorphic Structure Associated with Hurwitz-Lerch Zeta Function

Asian-European Journal of Mathematics
We investigate inclusion relationship of certain subclass of p-valent meromorphic functions defined in the punctured unit disc, having a pole of order p at the origin.
R. M. El-Ashwah, W. Y. Kota
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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 ...
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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
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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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The joint universality of Dirichlet L-functions and Lerch zeta-functions

Siberian Mathematical Journal, 2014
In this paper, the authors start from three fundamental dates for analytic number theory (ANT): {\parindent=6mm \begin{itemize}\item[-] in the 1837 Dirichlet introduced in ANT his ``\(L\)-functions'', with \(\chi=\chi\pmod q\) his characters: \[ L(s,\chi):=\sum_{n=1}^{\infty}\chi(n)/n^{s}; \] \item[-] in the 1857 Lipschitz generalized them (for ANT ...
Laurinčikas, A., Macaitienė, 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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Symmetry of zeros of Lerch zeta-function for equal parameters

, 2017
For most values of parameters λ and α, the zeros of the Lerch zeta-function L(λ, α, s) are distributed very chaotically. In this paper, we consider the particular case of equal parameters L(λ, λ, s) and show by calculations that the nontrivial zeros ...
R. Garunkštis, Rokas Tamosiunas
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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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