On the numerical evaluation of an oscillating infinite series
type: Item
instance of: scholarly article
title: On the numerical evaluation of an oscillating infinite series
zbMATH Open document ID: 0684.65003
DOI: 10.1016/0377-0427(89)90349-X
author: Münevver Tezer
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The series has the form \(\Sigma m\{m(m^ 2+u^ 2)^{-1}-1\}J_ 0(am)J_ 0(bm),\) where u, a, b are constants. This is not suitable for direct numerical evaluation because of the oscillation of the Bessel functions. It is transformed by contour integration and the ingenious use of Bessel function identities into a tractable form. Some results for special cases are presented in diagrams.
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 40A30
zbMATH DE Number: 4121268
zbMATH Keywords: oscillating infinite series
zbMATH Keywords: convergence acceleration
zbMATH Keywords: Bessel functions
MaRDI profile type: Publication
cites work: On certain integrals of Lipschitz-Hankel type involving products of bessel functions
cites work: Q4275389
cites work: Q5528526
description: scientific article; zbMATH DE number 4121268