On the Taylor expansion of the Lerch zeta-function
type: Item
instance of: scholarly article
title: On the Taylor expansion of the Lerch zeta-function
zbMATH Open document ID: 0763.11036
DOI: 10.1016/0022-247X(92)90034-B
author: Dieter Klusch
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-04-01T00:00:00Z
review text: The Lerch zeta function is the analytic continuation in the complex \(s\) plane of the series \[ L(x,a,s)=\sum_{n\geq 0}\exp\{2\pi inx\}(n+a)^{- s}, \] where \(x\) and \(a\) are real parameters. Properties of this function are deduced from its Taylor expansion in the parameter \(a\). By studying the function \(w(\xi)=L(x,\;a+\xi,\;s)\) in the neighborhood of \(\xi=0\) the author establishes a common source of various known summation formulas involving the Riemann zeta function \(\zeta(s)\) and the Hurwitz zeta function \(\zeta(s,a)\). The method also gives generalizations of some theorems that characterize these functions.
reviewed by: Tom M. Apostol
Mathematics Subject Classification ID: 11M35
zbMATH DE Number: 150668
zbMATH Keywords: Lerch zeta function
zbMATH Keywords: Taylor expansion
zbMATH Keywords: summation formulas
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: Hurwitz zeta function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 150668