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Semiclassical Multiple Orthogonal Polynomials and the Properties of Jacobi–Bessel Polynomials

✍ Scribed by A.I. Aptekarev; F. Marcellán; I.A. Rocha

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
429 KB
Volume
90
Category
Article
ISSN
0021-9045

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✦ Synopsis

This paper deals with Hermite Pade polynomials in the case where the multiple orthogonality condition is related to semiclassical functionals. The polynomials, introduced in such a way, are a generalization of classical orthogonal polynomials (Jacobi, Laguerre, Hermite, and Bessel polynomials). They satisfy a Rodrigues type formula and an (s+2)-order differential equation, where s is the class of the semiclassical functional. A special case of polynomials, multiple orthogonal with respect to the semiclassical weight function w(x)=x : 0 (x&a) : 1 e #Âx (a combination of the classical weights of Jacobi and Bessel), is analyzed in order to obtain the strong (Szego type) asymptotics and the zero distribution.

1997 Academic Press

1. Introduction

In the Introduction we present the basic notions, definitions, and notation of the paper. We sketch the history and the present state of the topic, and discuss the results obtained here.

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