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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 047, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.047 (Mi sigma1843) 		 
Determinantal Formulas for Exceptional Orthogonal Polynomials

Brian Simanek

Baylor University Math Department, Waco, Texas, 76706, USA
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DOI: https://doi.org/10.3842/SIGMA.2022.047
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.
Funding agency Grant number
Simons Foundation 707882
The author gratefully acknowledges support from the Simons Foundation through collaboration grant 707882.
Received: February 11, 2022; in final form June 17, 2022; Published online June 25, 2022
Bibliographic databases:
Document Type: Article
MSC: 42C05, 33C47
Language: English
Citation: Brian Simanek, “Determinantal Formulas for Exceptional Orthogonal Polynomials”, SIGMA, 18 (2022), 047, 16 pp.
Citation in format AMSBIB
\Bibitem{Sim22}
\by Brian~Simanek
\paper Determinantal Formulas for Exceptional Orthogonal Polynomials
\jour SIGMA
\yr 2022
\vol 18
\papernumber 047
\totalpages 16
\mathnet{http://mi.mathnet.ru/sigma1843}
\crossref{https://doi.org/10.3842/SIGMA.2022.047}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4444301}
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