Gauss-Legendre approximations for the Hubbell rectangular-source integral
type: Item
instance of: scholarly article
title: Gauss-Legendre approximations for the Hubbell rectangular-source integral
zbMATH Open document ID: 0826.65012
DOI: 10.1016/0377-0427(93)E0210-D
published in: Journal of Computational and Applied Mathematics
publication date: 1995-07-04T00:00:00Z
review text: Gauss-Legendre quadrature is used to generate some new approximation formulas for \(f(a,b)\), where \(f(a,b)\) is the Hubbell rectangular-source integral, \(0 < a \leq b <\infty\). Numerical values of \(f(a,b)\) are used in radiation physics applications. This function is closely related with Appell's hypergeometric function. The author presents a family of fairly efficient nonlinear approximations \(f(a,b) \approx \Omega_n (a,b)\), \(n = 1,2,\dots,\) that can be used to compute \(f(a,b)\) to a prescribed relative error, by taking \(n\) sufficiently large. The minimum number of significant decimal digits of accuracy attained by a particular approximation \(f(a,b) \approx \Omega_n (a,b)\), over the triangular domain \(0.1 \leq a \leq b \leq 20\), is ascertained from a table provided for the cases \(n = 1(1)4\) and \(6(2)16\).
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 33C65
Mathematics Subject Classification ID: 85A25
zbMATH DE Number: 770361
zbMATH Keywords: Gauss-Legendre quadrature
zbMATH Keywords: Hubbell rectangular-source integral
zbMATH Keywords: Appell's hypergeometric function
zbMATH Keywords: nonlinear approximations
author: Frank G. Lether
reviewed by: Grigori L. Litvinov
MaRDI profile type: Publication
cites work: Q5533688
cites work: Some expansions related to the Hubbell rectangular-source integral
cites work: Calculation of Gauss Quadrature Rules
cites work: On the construction of Gauss-Legendre quadrature rules
cites work: Q5535928
full work available at URL: 0377-0427(93)e0210-d
OpenAlex ID: W2055094403
description: scientific article; zbMATH DE number 770361