Orthogonal polynomials on two symmetric intervals
type: Item
instance of: scholarly article
title: Orthogonal polynomials on two symmetric intervals
zbMATH Open document ID: 0983.42017
DOI: 10.1007/BF02674209
author: N. P. Fadeev
published in: Mathematical Notes
publication date: 2002-04-16T00:00:00Z
review text: Given \(E=[-b,-a] \cup [a,b]\subset \mathbb R\) and an even weight function \(\rho\) on \(E\) satisfying a number of additional assumptions, the author establishes several algebraic properties of the corresponding orthogonal polynomials, such as a differential and an integral equation and a Rodrigues-type formula. In the particular case of \[ \rho (x)=|x|(b^2-x^2)^\alpha (x^2-a^2)^\beta , \quad \max (\alpha,\beta)\geq -1/2, \quad \alpha, \beta >-1, \] it is proved that the orthogonal polynomial of even degree attains the maximum of its absolute value at an endpoint of \(E\).
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1517563
zbMATH Keywords: orthogonal polynomial
zbMATH Keywords: differential equation
zbMATH Keywords: Rodrigues formula
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
cites work: Q3895800
full work available at URL: https://doi.org/10.1007/bf02674209
OpenAlex ID: W2048533844
description: scientific article; zbMATH DE number 1517563