Orthogonal polynomials and Stieltjes functions: the Laguerre-Hahn case
In this paper we consider orthogonal polynomials of the so-called Laguerre-Hahn class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a Riccati differential equation with polynomial coefficients. We introduce the concept of the order of the class f...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sapienza Università Editrice
1996-01-01
|
| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1996(1)/117-141.pdf |
| Summary: | In this paper we consider orthogonal polynomials of the so-called Laguerre-Hahn class. This means that the Stieltjes function associated with the corresponding moment sequence satisfies a Riccati differential equation with polynomial coefficients. We introduce the concept of the order of the class for a family of LaguerreHahn polynomials. Moreover, we find the order of the class for some finite perturbations of such a family of polynomials. Finally, some examples related to classical polynomials are given.
|
|---|---|
| ISSN: | 1120-7183 2532-3350 |