Plancherel-Rotach-type asymptotics for orthogonal polynomials associated with \(\exp (-x^ 6/6)\)
type: Item
instance of: scholarly article
title: Plancherel-Rotach-type asymptotics for orthogonal polynomials associated with \(\exp (-x^ 6/6)\)
zbMATH Open document ID: 0617.42017
DOI: 10.1016/0021-9045(87)90021-9
author: Rong-Chyu Sheen
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: Consider the weight \(f(x)=\exp (-x^ 6/6)\) on the real line and the associated sequence of orthonormal polynomials. The differential equation satisfied by this sequence is given and then used to find the strong asymptotic behavior of the orthonormal sequence. The solution to this problem for an arbitrary weight of the form \(f(x)-\exp (-x^{\lambda})\), \(\lambda >0\), was announced by \textit{E. A. Rakhmanov} in the Proceedings of the Second Conference of Orthogonal Polynomials and its Applications. Segovia 86 [to appear in Lect. Notes Math. (Springer-Verlag)].
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4000677
zbMATH Keywords: weight
zbMATH Keywords: orthonormal polynomials
zbMATH Keywords: strong asymptotic behavior
zbMATH Keywords: orthonormal sequence
reviewed by: Guillermo López Lagomasino
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90021-9
OpenAlex ID: W2001308969
cites work: A class of orthogonal polynomials
cites work: Q4092279
cites work: Q5677805
cites work: On polynomial approximation with the weight 363-1363-1363-1
cites work: Nonnegative solutions of a nonlinear recurrence
cites work: Asymptotics for Solutions of Smooth Recurrence Equations
cites work: Orthogonal polynomials
cites work: Q5186142
cites work: Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$
cites work: Exact bounds for orthogonal polynomials associated with exponential weights
cites work: Q3764454
description: scientific article; zbMATH DE number 4000677