On the summation of series in terms of Bessel functions
type: Item
instance of: scholarly article
title: On the summation of series in terms of Bessel functions
zbMATH Open document ID: 1102.33005
DOI: 10.4171/ZAA/1296
author: S. B. Tričković
author: M. V. Vidanović
author: Miomir S. Stanković
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2006-11-16T00:00:00Z
review text: This article deals with summation formulas for the series \[ \sum^\infty_{n=1} {J_\mu(nx)\over n^\nu}\tag{1} \] referring partly to some results from other paper of the same authors in [J. Math. Anal. Appl. 247, No. 1, 15--26 (2000; Zbl 0957.33003)]. At first the authors show how different summation formulas for the series (1) arise from integral representations of Bessel functions, Poisson's and Bessel's integral. Another representation of Bessel functions is considered and defined a suitable function to apply Poisson's formula and find one more summation formula for (1). It can be interesting for the rational approximation. See \textit{N. Hayek Calil}, \textit{P. González-Vera} and \textit{F. Pérez-Acosta} [Numer. Algorithms 3, No. 1--4, 235--244 (1992; Zbl 0784.65011)].
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 5073451
zbMATH Keywords: Bessel functions
zbMATH Keywords: Riemann's \(\xi\)-function
zbMATH Keywords: Poisson's formula
zbMATH Keywords: Fourier's transform
reviewed by: Francisco Pérez Acosta
MaRDI profile type: Publication
cites work: Q3331506
cites work: Q5736341
cites work: Q4515165
cites work: Q3916824
cites work: Q4059363
cites work: Q3744481
cites work: Q5647412
cites work: On the summation of series involving Bessel or Struve functions
description: scientific article; zbMATH DE number 5073451