Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials

TL;DR

This paper demonstrates that exceptional Charlier, Meixner, Hermite, and Laguerre polynomials satisfy higher order recurrence relations, proposing that these relations are of minimal order based on a constructive proof.

Contribution

It provides the first constructive proof that these exceptional orthogonal polynomials satisfy higher order recurrence relations, and conjectures their minimality.

Findings

Exceptional polynomials satisfy higher order recurrence relations

Recurrence relations are of minimal order (conjectured)

Constructive proof methodology used

Abstract

In this paper we prove in a constructing way that exceptional Charlier, Meixner, Hermite and Laguerre polynomials satisfy higher order recurrence relations. Our conjecture is that the recurrence relations provided in this paper have minimal order.