The Exceptional (X_{\ell}) (q)-Racah Polynomials
Satoru Odake, Ryu Sasaki
TL;DR
This paper constructs the exceptional Racah and q-Racah polynomials, completing the classification of all generic exceptional orthogonal polynomials of a single variable alongside previously discovered families.
Contribution
It introduces the exceptional Racah and q-Racah polynomials, expanding the family of known exceptional orthogonal polynomials and completing the classification.
Findings
Construction of exceptional Racah and q-Racah polynomials
They complete the set of generic exceptional orthogonal polynomials
Unified framework with previously known exceptional polynomials
Abstract
The exceptional Racah and q-Racah polynomials are constructed. Together with the exceptional Laguerre, Jacobi, Wilson and Askey-Wilson polynomials discovered by the present authors in 2009, they exhaust the generic exceptional orthogonal polynomials of a single variable.
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