On the asymptotic distribution of the zeros of Hermite, Laguerre, and Jonquière polynomials
type: Item
instance of: scholarly article
title: On the asymptotic distribution of the zeros of Hermite, Laguerre, and Jonquière polynomials
zbMATH Open document ID: 0629.42012
DOI: 10.1016/0021-9045(87)90020-7
author: Wolfgang Gawronski
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: The author presents an alternative derivation of the contracted zero distribution of the Hermite and Laguerre polynomials. He also derives the zero distribution of the Jonquière polynomials, \(P_ n(z)\), defined by \(P_ n(z):= (1-z)^ n\sum^{\infty}_{j=1}j^ nz^ j,\) \(n=1,2,3,... \). \(P_ n(z)\) is a polynomial of degree n, having n simple zeros in (- \(\infty,0]\). Some other generalisations of Jonquière polynomials are also considered.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 30E15
zbMATH DE Number: 4023960
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: zero distribution
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Jonquière polynomials
reviewed by: Doron S. Lubinsky
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90020-7
OpenAlex ID: W2088643735
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description: scientific article; zbMATH DE number 4023960