An algebraic treatment of the Askey biorthogonal polynomials on the unit circle

Abstract

A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra mJ.

A note on $\mathfrak{su}(2)$ models and the biorthogonality of generating functions of Krawtchouk polynomials

“…Of course if the operators involved are self-adjoint the solutions associated to different eigenvalues are simply orthogonal. In the investigation of the algebraic description of certain families of biorthogonal functions [2], [3], we were led to observations pertaining to the generating functions of the Krawtchouk polynomials [4] that prompted this note.…”