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Asymptotic behavior of the Lerch transcendent function [PDF]

Journal of Approximation Theory, 2013
For complex parameters and s, consider the Lerch transcendent (,s,z)=k=0k(k+z)-s as a function of the complex variable. z. We analyze the asymptotic behavior of this function as Re s - . © 2012 Elsevier Inc.
Luis M Navas, FRANCISCO J Ruiz, Juan L Varona   +2 more
exaly   +6 more sources

The Lerch zeta function I. Zeta integrals [PDF]

Forum Mathematicum, 2012
Abstract. This is the first of four papers that study algebraic and analytic structures associated to the Lerch zeta function. This paper studies “zeta integrals” associated to the Lerch zeta function using test functions, and obtains functional equations for them.
Jeffrey C Lagarias, Wen-Ching Winnie Li
exaly   +4 more sources

The Lerch zeta function II. Analytic continuation [PDF]

Forum Mathematicum, 2012
Abstract. This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. The Lerch zeta function (
Jeffrey C Lagarias, Wen-Ching Winnie Li
exaly   +4 more sources

Note on the Hurwitz–Lerch Zeta Function of Two Variables [PDF]

Symmetry, 2020
Choi, Junesang/0000-0002-7240-7737; Yagci, Oguz/0000-0001-9902-8094A number of generalized Hurwitz-Lerch zeta functions have been presented and investigated.
Junesang Choi, Recep Şahin, Oguz Yagci   +2 more
exaly   +2 more sources

A Quadruple Definite Integral Expressed in Terms of the Lerch Function

Symmetry, 2021
A quadruple integral involving the logarithmic, exponential and polynomial functions is derived in terms of the Lerch function. Special cases of this integral are evaluated in terms of special functions and fundamental constants.
, Allan Stauffer, Reynolds Robert
exaly   +2 more sources

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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.
openaire   +1 more source

A Double Logarithmic Transform Involving the Exponential and Polynomial Functions Expressed in Terms of the Hurwitz–Lerch Zeta Function

Symmetry, 2021
The object of this paper is to derive a double integral in terms of the Hurwitz–Lerch zeta function. Almost all Hurwitz–Lerch zeta functions have an asymmetrical zero-distribution. Special cases are evaluated in terms of fundamental constants.
, Allan Stauffer, Reynolds Robert
exaly   +2 more sources

On the Hurwitz—Lerch zeta-function

Aequationes Mathematicae, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kanemitsu, Shigeru, Katsurada, Masanori, Yoshimoto, Masami   +2 more
openaire   +1 more source

Asymptotic expansions of the Hurwitz–Lerch zeta function

Journal of Mathematical Analysis and Applications, 2004
In the paper, a generalization of the asymptotic expansions obtained by \textit{M.~Katsurada} [Proc.~Japan Acad. 74, No. 10, 167--170 (1998; Zbl 0937.11035)] and \textit{D.~Klusch} [J.~Math. Anal. Appl. 170, No. 2, 513--523 (1992; Zbl 0763.11036)] for the Lipschitz-Lerch zeta function \[ R(a, x, s)\equiv\sum_{k=0}^\infty {e^{2k\pi ix}\over (a+k)^s ...
JOSÉ L Lopez
exaly   +3 more sources

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.
openaire   +2 more sources