Numerical evaluation of spherical Bessel functions of the first kind
type: Item
instance of: scholarly article
title: Numerical evaluation of spherical Bessel functions of the first kind
zbMATH Open document ID: 0804.65022
author: Aleksander Jablonski
published in: Journal of Computational Physics
publication date: 1995-01-15T00:00:00Z
review text: The paper discusses five algorithms (series expansion, forward recursion, backward recursion, analytical solution, phase and amplitude representation) for computing the spherical Bessel functions \(j(x)\) for real values of \(x\). The first four algorithms are selected for developing a universal and reliable algorithm. Reviewer's remark: The author says: It turns out that the usual algorithms providing the values of the spherical Bessel functions of the fiirst kind, \(j_ l (x)\), have a rather limited range of stability. The author does not show where the cited references fail in this respect. Also, the author seems to be unaware of the set of algorithms developed by \textit{D. E. Amos} [ACM Trans. Math. Software 12, 265-273 (1986; Zbl 0613.65013)] because this important reference would have given the author a different opinion about the availability of reliable software for the Bessel functions.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 569500
zbMATH Keywords: series expansion
zbMATH Keywords: forward recursion
zbMATH Keywords: backward recursion
zbMATH Keywords: analytical solution
zbMATH Keywords: phase and amplitude representation
zbMATH Keywords: spherical Bessel functions
zbMATH Keywords: universal and reliable algorithm
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: jcph.1994.1060
OpenAlex ID: W2070347250
DOI: 10.1006/JCPH.1994.1060
description: scientific article; zbMATH DE number 569500