4 papers · 1 filter
Classical Heun observables and elliptic solvability
Luc Vinet, Alexei Zhedanov
We introduce a classical analog of the algebraic Heun operator associated with a classical Leonard pair. Given two observables and satisfying the classical counterpart of t…
The rank two Jacobi algebra
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is s…
Meta Algebras and Biorthogonal Rational Functions: The Hahn Case
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
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 met…
The Onsager algebra and multivariable special functions
Pascal Baseilhac, Luc Vinet, Alexei Zhedanov
Two sets of mutually commuting difference operators and , such that and generate a homomorphic image of the Onsager algebra for each $…