The symmetric D_w-Laguerre–Hahn orthogonal polynomial of class one

ABSTRACT

We give the system of Laguerre–Freud equations for the recurrence coefficients ${\beta }_n$, ${\gamma }_{n+1}$, $n\ge 0$, of orthogonal polynomials with respect to a $D_w$-Laguerre–Hahn form (linear functional) of class one, where $D_w$ is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases.

KEYWORDS:

• Discrete Laguerre–Hahn orthogonal polynomials
• difference operator

MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 33C45
• Secondary 42C05

Acknowledgments

The authors thank the referee(s) for their valuable comments and their careful reading of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).