106 citations · 956 across the 40 of their papers we have counts for
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Coupling coefficients of and multivariate -Racah polynomials
Vincent X. Genest, Plamen Iliev, Luc Vinet
Gasper & Rahman's multivariate -Racah polynomials are shown to arise as connection coefficients between families of multivariate -Hahn or -Jacobi polynomials. The families…
Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials
Vincent X. Genest, Satoshi Tsujimoto, Luc Vinet +1
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed.…
An algebraic interpretation of the multivariate -Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet
The multivariate quantum -Krawtchouk polynomials are shown to arise as matrix elements of "-rotations" acting on the state vectors of many -oscillators. The focus is put o…
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke al…
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra
Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet +1
The algebraic underpinning of the tridiagonalization procedure is investigated. The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadrat…
Two-variable Jacobi polynomials
Vincent X. Genest, Jean-Michel Lemay, Luc Vinet +1
A two-variable generalization of the Big Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate…
A "Continuous" Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A novel family of orthogonal polynomials called the Chihara polynomials is characterized. The polynomials are obtained from a "continuous" limit of the complementary Bannai-It…