Norm behavior and zero distribution for orthogonal polynomials with nonsymmetric weights
type: Item
instance of: scholarly article
title: Norm behavior and zero distribution for orthogonal polynomials with nonsymmetric weights
zbMATH Open document ID: 0667.42010
DOI: 10.1007/BF01889613
published in: Constructive Approximation
publication date: 1989-01-01T00:00:00Z
review text: The asymptotic behavior of the nth root of the leading coefficient of orthogonal polynomials on (-\(\infty,\infty)\) and the distribution of their zeros is studied for nonsymmetric weights that behave like \(\exp (- 2Ax^{\alpha})\) when \(x>0\) and \(\exp (-2B| x|^{\alpha})\) when \(x<0\), where \(A\neq B\). These results generalize previous investigations of Rakhamanov and Mhaskar and Saff who handle the symmetric case \(A=B\).
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4092078
zbMATH Keywords: logarithmic potential
zbMATH Keywords: regular variation
zbMATH Keywords: Meixner-Pollaczek polynomials
zbMATH Keywords: orthogonal polynomials
author: Walter Van Assche
MaRDI profile type: Publication
cites work: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
cites work: Q4726487
cites work: DUALITY FOR REGULARLY VARYING FUNCTIONS
cites work: Invariant sets under iteration of rational functions
cites work: Q4170993
cites work: Q3258458
cites work: EQUILIBRIUM MEASURE AND THE DISTRIBUTION OF ZEROS OF EXTREMAL POLYNOMIALS
cites work: Q4275389
cites work: Q5748345
cites work: Freud’s conjecture for exponential weights
cites work: A proof of Freud's conjecture for exponential weights
cites work: Strong asymptotics for extremal polynomials associated with weights on \({\mathbb{R}}\)
cites work: Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion
cites work: Extremal Problems for Polynomials with Exponential Weights
cites work: Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$
cites work: On Asymptotic Average Properties of Zeros of Orthogonal Polynomials
cites work: Q5798212
cites work: ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE REAL AXIS
cites work: Regularly varying functions
cites work: Q4061445
cites work: On the Regular Behaviour of Orthogonal Polynomials
cites work: Orthogonal polynomials associated with an infinite interval
cites work: Q3759152
cites work: Asymptotics for orthogonal polynomials
cites work: Asymptotic properties of orthogonal polynomials from their recurrence formula. II
cites work: Asymptotics for orthogonal polynomials with regularly varying recurrence coefficients
full work available at URL: https://doi.org/10.1007/bf01889613
OpenAlex ID: W2082880950
description: scientific article; zbMATH DE number 4092078