Determinantal Formulas for Exceptional Orthogonal Polynomials

TL;DR

This paper derives determinantal formulas for exceptional orthogonal polynomials, including Laguerre, Jacobi, and Hermite types, using zeros of classical polynomials, which simplifies their computation and analysis.

Contribution

It introduces new determinantal formulas for exceptional orthogonal polynomials, expanding the mathematical tools available for their study.

Findings

Determinantal formulas for exceptional Laguerre, Jacobi, and Hermite polynomials.

Formulas resemble Vandermonde determinants and involve zeros of classical polynomials.

Provides a unified approach to compute and analyze exceptional orthogonal polynomials.

Abstract

We present determinantal formulas for families of exceptional $X_m$-Laguerre and exceptional $X_m$-Jacobi polynomials and also for exceptional $X_2$-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of the classical orthogonal polynomials.