Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights
type: Item
instance of: scholarly article
title: Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights
zbMATH Open document ID: 0991.42016
DOI: 10.1023/A:1006625030000
published in: Acta Mathematica Hungarica
publication date: 2000-05-14T00:00:00Z
review text: The author proves uniform asymptotic formulae when \(n\to\infty\) on the unit circle for derivatives of (complex) orthogonal polynomials based on Jacobi-type weights with a finite number of power type singularities. The corollaries of these results settle the corresponding problems for generalized Jacobi polynomials on \([-1, 1]\), that is, for the (real) orthogonal polynomials based on power type weights with inner singularities. The results are based on the works of \textit{G. Szegő} [``Orthogonal polynomials'' (1939; Zbl 0023.21505) ] and \textit{V. M. Badkov} [Proc. Steklov Inst. Math. 198, 37-82 (1994; Zbl 0824.42020)].
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1446761
zbMATH Keywords: weights
zbMATH Keywords: derivatives
zbMATH Keywords: asymptotic formulae
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Jacobi-type weights
author: Péter Vértesi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1446761