On the complex zeros of some families of orthogonal polynomials
type: Item
instance of: scholarly article
title: On the complex zeros of some families of orthogonal polynomials
zbMATH Open document ID: 1200.30002
DOI: 10.1155/2010/263860
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/229868
review text: Summary: The complex zeros of the orthogonal Laguerre polynomials \(L_n^{(a)}(x)\) for \(a<-n\), ultraspherical polynomials \(P_n^{(\lambda)}(x)\) for \(\lambda<-n\), Jacobi polynomials \(P_n^{(a,\beta)}(x)\) for \(a<-n\), \(\beta<-n\), \(a+\beta<-2(n+1)\), orthonormal Al-Salam-Carlitz II polynomials \(P_n^{(a)}(x;q)\) for \(a<0\), \(0<q<1\), and \(q\)-Laguerre polynomials \(L_n^{(a)}(x;q)\) for \(a<-n\), \(0<q<1\) are studied. Several inequalities regarding the real and imaginary properties of these zeros are given, which help locating their position. Moreover, a few limit relations regarding the asymptotic behavior of these zeros are proved. The method used is a functional analytic one. The obtained results complement and improve previously known results.
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 5791611
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Jacobi polynomials
Wikidata QID: Q58649803
author: Eugenia N. Petropoulou
MaRDI profile type: Publication
OpenAlex ID: W2100709563
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description: scientific article; zbMATH DE number 5791611