Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
type: Item
instance of: scholarly article
title: Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
zbMATH Open document ID: 0795.33001
DOI: 10.1016/0377-0427(93)90168-B
author: A. Zarzo
author: A. Ronveaux
author: Eduardo Godoy
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-01T00:00:00Z
review text: A program built in the symbolic language of Mathematica is given, which is able to calculate the unique differential equation satisfied by the associate (of any order) of one of the four classical systems of polynomials (Jacobi, Hermite, Laguerre, Bessel). The associates are polynomials satisfying the same 3-term recurrence relation as the original system of polynomials, but with shifted coefficients. The differential equation is used to study the distribution of the zeros of the associated polynomials via Newton sum rules.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33-04
zbMATH DE Number: 540482
zbMATH Keywords: zeros
zbMATH Keywords: associated polynomials
reviewed by: Herbert Stahl
MaRDI profile type: Publication
Wikidata QID: Q115363244
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description: scientific article; zbMATH DE number 540482