Accurate evaluation of an integral involving the product of two Bessel functions and a Gaussian
type: Item
instance of: scholarly article
title: Accurate evaluation of an integral involving the product of two Bessel functions and a Gaussian
zbMATH Open document ID: 0605.65012
DOI: 10.1016/0021-9991(87)90047-7
author: E. S. Hirschorn
author: George H. Rawitscher
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: An integral of the form \(G(L)=\int^{R}_{0}f_ 1(r)V(r)f_ 2(r)dr\) is numerically evaluated, where \(f_ i(r)=K_ irJ_ L(K_ ir)\), \(i=1,2\), and \(V(r)=\exp (-r^ 2/a^ 2)\) with real numbers R and r, complex numbers \(K_ i\), and spherical Bessel functions \(J_ L\) of \(K_ ir\). This algorithm makes use of a recursion relation between G(L), \(G(L+1)\) and G(L-1) together with the values of G for \(L=0\) and \(L=1\). This idea comes from the fact that the values of G(-1) and G(0) are analytically expressed in terms of error functions and easily calculatable by means of a continued fraction with few error.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33E99
zbMATH DE Number: 3978261
zbMATH Keywords: numerical examples
zbMATH Keywords: Bessel integral
zbMATH Keywords: recursion relation
zbMATH Keywords: error function
zbMATH Keywords: continued fraction
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90047-7
OpenAlex ID: W1975946719
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description: scientific article; zbMATH DE number 3978261