An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type

Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei

doi:10.1090/proc/15225

An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type
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Proc. Amer. Math. Soc. 149 (2021), 715-728 Request permission

Abstract:

The biorthogonal rational functions of ${_3}F_2$ type on the uniform grid provide the simplest example of rational functions with bispectrality properties that are similar to those of classical orthogonal polynomials. These properties are described by three difference operators $X,Y,Z$ which are tridiagonal with respect to three distinct bases of the relevant finite-dimensional space. The pairwise commutators of the operators $X,Y,Z$ generate a quadratic algebra which is akin to the algebras of Askey–Wilson type attached to hypergeometric polynomials.

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