Numerical computation of incomplete Lipschitz-Hankel integral \(Je_ 0(a,z)\)
type: Item
instance of: scholarly article
title: Numerical computation of incomplete Lipschitz-Hankel integral \(Je_ 0(a,z)\)
zbMATH Open document ID: 0701.65012
DOI: 10.1016/0021-9991(90)90255-Y
author: Steven L. Dvorak
author: Edward F. Kuester
published in: Journal of Computational Physics
publication date: 1990-01-01T00:00:00Z
review text: Incomplete Lipschitz-Hankel integrals are important special functions since they arise in a number of problems in mathematical physics. The authors consider especially the integral \(\int^{z}_{0}e^{-at}J_ 0(t)dt\), \(J_ 0\) the Bessel function. Convergent and asymptotic factorial-Neumann series expansions are used in an algorithm for computing the integral to a user defined number of significant digits. [A ``factorial-Neumann series'' can be written in the form \(\Sigma a_ nz^ nJ_{n+r}(z)\). \textit{N. Nielsen} in the classical ``Handbuch der Theorie der Cylinderfunktionen'', (1904; JFM 35.0476.03) classified this series as ``Fakultätenreihe'', different from the usual terminology, due to E. Landau a.o..] The algorithm offers a very accurate and efficient way to compute the integral, particularly when compared with an adaptive quadrature routine. The algorithm accomplishes this by choosing automatically which of the asymptotic expansions to use.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33D60
zbMATH DE Number: 4149441
zbMATH Keywords: Incomplete Lipschitz-Hankel integrals
zbMATH Keywords: Bessel function
zbMATH Keywords: asymptotic factorial-Neumann series expansions
zbMATH Keywords: FdM 35, 476
zbMATH Keywords: algorithm
zbMATH Keywords: adaptive quadrature routine
zbMATH Keywords: asymptotic expansions
MaRDI profile type: Publication
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full work available at URL: 0021-9991(90)90255-y
OpenAlex ID: W1975760886
description: scientific article; zbMATH DE number 4149441