Une caractérisation des polynômes strictement 1/p orthogonaux de type Scheffer. Étude du cas \(p=2\). (A characterization of strictly 1/p orthogonal polynomials of Scheffer type)
type: Item
instance of: scholarly article
title: Une caractérisation des polynômes strictement 1/p orthogonaux de type Scheffer. Étude du cas \(p=2\). (A characterization of strictly 1/p orthogonal polynomials of Scheffer type)
zbMATH Open document ID: 0662.42018
DOI: 10.1016/0021-9045(88)90117-7
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: A sequence \(\{P_ n(x)\}\), \(n\geq 0\), of polynomials is called of type A zero if it is defined by means of a generating function of the form \(G(x,t)=A(t)e^{xH(t)}=\sum_{n\geq 0}P_ n(x)t^ n/n!\). Sequences of such type are considered, which are strictly 1/p orthogonal (p\(\geq 2\) fixed) and a characterization is given by means of two differential equations satisfied by A and H respectively. In only one of the two cases which arise the sequence of polynomials \(P_ n\) satisfy a \(p+1\)-term recurrence relation. With the results obtained it is shown that there are exactly nine families of strictly semi-orthogonal polynomials satisfying three term recurrence relations and five families which satisfy four term recurrence relations.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4082222
zbMATH Keywords: strictly semi-orthogonal polynomials
zbMATH Keywords: three term recurrence relations
author: Ammar Boukhemis
author: P. Maroni
reviewed by: Guillermo López Lagomasino
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90117-7
OpenAlex ID: W2241385648
cites work: Convergence of generalized c-fractions
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cites work: Some properties of polynomial sets of type zero
description: scientific article; zbMATH DE number 4082222