Asymptotics and bounds for the zeros of Laguerre polynomials: A survey
type: Item
instance of: scholarly article
title: Asymptotics and bounds for the zeros of Laguerre polynomials: A survey
zbMATH Open document ID: 1008.65011
DOI: 10.1016/S0377-0427(01)00549-0
author: Luigi Gatteschi
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: The zeros of the Laguerre polynomial \(L_n^{(\alpha)}(x)\) are considered for large values of the quantity \(\nu=4n+2\alpha+2\), including the cases when one or both parameters \(n\) and \(\alpha\) are large. An overview is given for bounds and for asymptotic approximations of the zeros. New uniform approximations are given in terms of zeros of a Bessel function and of the Airy function. Numerical results and graphical comparisons are provided.
reviewed by: Nico M. Temme
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33F05
zbMATH DE Number: 1787645
zbMATH Keywords: Laguerre polynomial
zbMATH Keywords: asymptotics of zeros
zbMATH Keywords: bounds of zeros
zbMATH Keywords: Bessel function
zbMATH Keywords: Airy function
zbMATH Keywords: Hermite polynomial
zbMATH Keywords: Whittaker function
zbMATH Keywords: uniform asymptotic approximation
zbMATH Keywords: Liouville-Green transform
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787645