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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2022 Volume 18, 047, 16 pp. (Mi sigma1843)

Determinantal Formulas for Exceptional Orthogonal Polynomials

Brian Simanek

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

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.

Keywords: exceptional orthogonal polynomials, determinantal formulas.

MSC: 42C05, 33C47

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

Language: English

DOI: 10.3842/SIGMA.2022.047



Bibliographic databases:
ArXiv: 2202.01278


© Steklov Math. Inst. of RAS, 2024