Bounds for zeros of the Laguerre polynomials
type: Item
instance of: scholarly article
title: Bounds for zeros of the Laguerre polynomials
zbMATH Open document ID: 1018.33008
DOI: 10.1016/S0021-9045(03)00029-7
published in: Journal of Approximation Theory
publication date: 2003-05-27T00:00:00Z
review text: The author shows that the least and largest zeros \(x_1, x_n\) of the Laguerre polynomial \(L_n ^{(\alpha)}(x)\) satisfies \[ x_1 > s-r + {(s-r)^{2/3} \over 2r^{1/3}} \] \[ x_n < s+r + {(s+r)^{2/3} \over 2r^{1/3}} \] with \[ s=2n+ \alpha +1, \;r= \sqrt{4n^2 +(2n-1)(2 \alpha +2)} \] provided \(n\geq 7, \alpha \geq 8\).
reviewed by: W. Koepf
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1917878
zbMATH Keywords: zeros of the Laguerre polynomials
zbMATH Keywords: Airy function
author: Ilia Krasikov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1917878