Determinantal Formulas for 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.

References in corpus (7)

• Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
• Exceptional Jacobi polynomials
• Exceptional Laguerre polynomials
• Exceptional Legendre Polynomials and Confluent Darboux Transformations
• Spectral analysis for the exceptional $X_m$-Jacobi equation
• Moment Representations of Exceptional $X_1$ Orthogonal Polynomials
• Moment Representations of the Exceptional $X_1$-Laguerre Orthogonal Polynomials