Orthogonal polynomials and Stieltjes functions: the Laguerre-Hahn case

Abstract

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.

Keywords

• quasi-definite linear functions
• orthogonal polynomials
• recurrence relations
• finite perturbations
• stieltjes functions