Meta Algebras and Biorthogonal Rational Functions: The Hahn Case

Abstract

The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated meta Hahn algebra and its finite-dimensional representations. The functions of interest arise as overlaps between eigensolutions of generalized and ordinary eigenvalue problems on the representation space. The orthogonality relations and bispectral properties naturally follow from the framework.

References in corpus (6)

• The Askey-Wilson algebra and its avatars
• Dualities in the $q$-Askey scheme and degenerate DAHA
• Two-generated algebras and standard-form congruence
• Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
• Bispectrality and biorthogonality of the rational functions of $q$-Hahn type
• Charting the $q$-Askey scheme. II. The $q$-Zhedanov scheme