A new recurrence formula for generic exceptional orthogonal polynomials

TL;DR

This paper introduces a novel recurrence relation applicable to all three types of exceptional orthogonal polynomials, with explicit examples for Xj-Hermite, Laguerre, and Jacobi polynomials.

Contribution

It presents a new recurrence formula that unifies the treatment of type 1, 2, and 3 exceptional orthogonal polynomials, with concrete examples.

Findings

Recurrence relation valid for type 1, 2, and 3 exceptional polynomials

Explicit recurrence formulas for Xj-Hermite, Laguerre, and Jacobi polynomials

Enhances understanding of structure and computation of exceptional orthogonal polynomials

Abstract

A new recurrence relation for exceptional orthogonal polynomials is proposed, which holds for type 1, 2 and 3. As concrete examples, the recurrence relations are given for Xj-Hermite, Laguerre and Jacobi polynomials in j = 1,2 case.