On the classical \(d\)-orthogonal polynomials defined by certain generating functions. I
type: Item
instance of: scholarly article
title: On the classical \(d\)-orthogonal polynomials defined by certain generating functions. I
zbMATH Open document ID: 0945.33007
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2000-10-08T00:00:00Z
review text: The paper is devoted to \(d\)-orthogonal polynomials \((p_n)_{n\in \mathbb{N}}\) defined by \[ \sum^\infty_{n=0} a_n\bigl[(d+1) xt-t^{d+1} \bigr]= \sum^\infty_{n=0} b_np_n (x)t^n , \] where \(d\) is a fixed positive integer. It is proved that the polynomials \((p_n)_{n \in\mathbb{N}}\) are \(d\)-symmetric and ``classical'' in the Hahn's sense. Finally, some properties of the zeros of the polynomials \((p_n)_{n\in \mathbb{N}}\) as well as a \((d+1)\)-order differential equation satisfied by each polynomial are given.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1423100
zbMATH Keywords: generating functions
zbMATH Keywords: Hermite polynomials
zbMATH Keywords: Gegenbauer polynomials
zbMATH Keywords: \(d\)-orthogonal polynomials
author: Youssèf Ben Cheikh
author: Khalfa Douak
reviewed by: J. Saurer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1423100