# Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one

- Authors
- Type
- Published Article
- Journal
- Advances in Pure and Applied Mathematics
- Publisher
- De Gruyter
- Publication Date
- Sep 11, 2018
- Volume
- 10
- Issue
- 4
- Pages
- 395–411
- Identifiers
- DOI: 10.1515/apam-2018-0015
- Source
- De Gruyter
- Keywords
- License
- Yellow

## Abstract

We give the system of Laguerre–Freud equations for the recurrence coefficients β n {\beta_{n}} , γ n + 1 {\gamma_{n+1}} , n ≥ 0 {n\geq 0} , of orthogonal polynomials with respect to a D-Laguerre–Hahn form (linear functional) of class one. The system is solved in the case when β 0 = - θ 0 {\beta_{0}=-\theta_{0}} , β n + 1 = θ n - θ n + 1 {\beta_{n+1}=\theta_{n}-\theta_{n+1}} and γ n + 1 = - θ n 2 {\gamma_{n+1}=-\theta_{n}^{2}} with θ n ≠ 0 {\theta_{n}\neq 0} , n ≥ 0 {n\geq 0} . There are essentially three canonical cases.