On the coefficients of Neumann series of Bessel functions
type: Item
instance of: scholarly article
title: On the coefficients of Neumann series of Bessel functions
zbMATH Open document ID: 1220.33003
author: D. Jankov
author: Tibor K. Pogány
author: Endre Süli
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-05-16T00:00:00Z
review text: In this note the authors describe the class \(\Lambda=\{\alpha\}\) of functions that generate the integral representation of a Neumann series of Bessel functions, in the sense that the restriction \(\alpha|_{\mathbb N}=(\alpha_{n})\) forms the coefficient array of the series \[ {\mathcal N}_{\nu}(z)=\sum_{n=1}^{\infty}\alpha_{n}J_{\nu+n}(z), \quad z\in \mathbb C, \] where \(\nu\), \(\alpha_n\) are constants and \(J_\mu\) is the Bessel function of the first kind and order \(\mu\). Knowing only the set of nodes \(N:=\{(n,\alpha_n)\}_{n\in\mathbb N}\), this question cannot be answered merely by examining the convergence of the series \({\mathcal N}_\nu(z)\) and then interpolating the set \(N\). The authors formulate an answer to this question so that the resulting class of functions \(\alpha\) depends on a suitable, integrable on \(\mathbb R_+\), scaling-function \(h\).
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 40A30
zbMATH DE Number: 5888549
zbMATH Keywords: Neumann series of Bessel functions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.02.065
OpenAlex ID: W2029512223
cites work: Q4514952
cites work: Integral representation for Neumann series of Bessel functions
cites work: Neumann Series of Bessel Functions
cites work: Neumann Series of Bessel Functions. II
DOI: 10.1016/J.JMAA.2011.02.065
description: scientific article; zbMATH DE number 5888549