Results 161 to 170 of about 26,951 (214)

On the lerch zeta-function

Lithuanian Mathematical Journal, 1996
Let \(s= \sigma+it\) be a complex variable, and let \(\mathbb{R}\) and \(\mathbb{Z}\) denote the sets of all real numbers and all integer numbers, respectively. Then the Lerch zeta-function is defined by \[ L(\lambda, \alpha,s) =\sum^\infty_{m=0} {e^{2 \pi i\lambda m} \over (m+ \alpha)^s} \quad \text{for} \quad \sigma>1, \] where \(\lambda \in\mathbb{R}
Garunkštis, R., Laurinčikas, A.
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Twists of Lerch Zeta-Functions

Lithuanian Mathematical Journal, 2001
This paper is on some basic properties of twists of Lerch zeta-functions defined as \[ L(\lambda, \alpha, s, \chi, Q) = \sum_{n=0}^{\infty}{\chi(n+Q)e^{2\pi i\lambda n}\over (n+\alpha)^{s}} \quad (\Re s > 1), \] where \(0 < \alpha\leq 1\), \(\lambda\in \mathbb R\), \(Q\in \mathbb Z\) and \(\chi\) is a Dirichlet character to the modulus \(q\).
Garunkštis, R., Steuding, J.
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On the Hurwitz—Lerch zeta-function

Aequationes Mathematicae, 2000
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Kanemitsu, Shigeru, Katsurada, Masanori, Yoshimoto, Masami   +2 more
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Approximation of analytic functions by generalized shifts of the Lerch zeta-function

Mathematical Modelling and Analysis
In the paper, we approximate analytic functions by generalized shifts $L(\lambda, \alpha, s+ig(\tau))$, $s=\sigma+it$, of the Lerch zeta-function, where $g$ is a certain increasing to $+\infty$ real function having a monotonic derivative.
A. Balčiūnas, Toma Mikalauskaitė, D. Šiaučiūnas   +2 more
semanticscholar   +1 more source

Generating Function Involving General Function Related to Hurwitz- Lerch Zeta Function

Communications on Applied Nonlinear Analysis
In this paper, we have studied a general function which unifies the Hurwitz-Lerch Zeta function and Mittage-Leffler function. The integral representation of the function and certain generating functions involving this general function are established.
B. B. Jaimini
semanticscholar   +1 more source

Caputo Derivative Formulas of Hurwitz-Lerch Zeta Function and Applications

Communications on Applied Nonlinear Analysis
In this paper, we find the fractional derivative formulas of Hurwitz-Lerch Zeta function. Further, we compute the solution of fractional differential equations involving Hurwitz-Lerch Zeta function.
Sandeep Kumar, Owais Khan, N. U. Khan, N. Ahmad   +3 more
semanticscholar   +1 more source

Fuzzy Treatment for Meromorphic Classes of Admissible Functions Connected to Hurwitz-Lerch Zeta Function

Axioms
Fuzzy differential subordinations, a notion taken from fuzzy set theory and used in complex analysis, are the subject of this paper. In this work, we provide an operator and examine the characteristics of meromorphic functions in the punctured open unit ...
Ekram E. Ali, R. El-ashwah, A. Albalahi, Rabab Sidaoui   +3 more
semanticscholar   +1 more source

The Approximation of Analytic Functions Using Shifts of the Lerch Zeta-Function in Short Intervals

Axioms
In this paper, we obtain approximation theorems of classes of analytic functions by shifts L(λ,α,s+iτ) of the Lerch zeta-function for τ∈[T,T+H] where H∈[T27/82,T1/2]. The cases of all parameters, λ,α∈(0,1], are considered.
Antanas Laurinčikas
semanticscholar   +1 more source

An Approximate Functional Equation for the Lerch Zeta Function

Mathematical Notes, 2003
Let \(01\), is defined by \[ L(\lambda,\alpha,s)=\sum_{n=0}^{\infty}\frac{e^{2 \pi i \lambda n}}{(n+\alpha)^s}.
Garunkštis, R., Laurinčikas, A., Steuding, J.   +2 more
openaire   +2 more sources

Certain Integral Representation and Fractional Derivatives Associated to a General Function Related to Hurwitz-Lerch Zeta Function

Panamerican Mathematical Journal
In this paper, some integral representation and fractional derivatives of a general function are established. The general function studied in this paper unifies the Mittag-Leffler function and the Hurwitz-Lerch Zeta function.
B. B. Jaimini
semanticscholar   +1 more source