Monotonicity results on the zeros of generalized Laguerre polynomials
type: Item
instance of: scholarly article
title: Monotonicity results on the zeros of generalized Laguerre polynomials
zbMATH Open document ID: 0645.33013
DOI: 10.1016/0021-9045(87)90031-1
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: Let \(L_ n^{(\alpha)}(x)\) be the generalized Laguerre polynomial. The authors prove two theorems on the zeros of this polynomial. We state: Theorem 1. For \(-1<\alpha \leq 1\) and \(k=1,2,...,n\), let \(x_{nk}=x_{nk}(\alpha)\) be the kth positive zero of the generalized Laguerre polynomial \(L_ n^{(\alpha)}(x)\) in increasing order. Then \((n+(\alpha +1)/2)x_{nk}+(1/4)x^ 2_{nk}\) increases with n.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 4052015
zbMATH Keywords: generalized Laguerre polynomial
author: Á. Elbert
author: A. Laforgia
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90031-1
OpenAlex ID: W1964580216
cites work: On the Spacing of the Zeros of Some Classical Orthogonal Polynomials
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cites work: Turánians and Wronskians for the Zeros of Bessel Functions
description: scientific article; zbMATH DE number 4052015