Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 047, 16 pages      arXiv:2202.01278

Determinantal Formulas for Exceptional Orthogonal Polynomials

Brian Simanek
Baylor University Math Department, Waco, Texas, 76706, USA

Received February 11, 2022, in final form June 17, 2022; Published online June 25, 2022

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.

Key words: exceptional orthogonal polynomials; determinantal formulas.

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