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Eigenvalue equations for sieved polynomials or proving Askey right again
Luc Vinet, Alexei Zhedanov
The sieved Jacobi polynomials have been introduced by Askey. These can be obtained from conveniently taking to be a root of unity in the Askey-Wilson polynomials. The question…
Bispectrality of the sieved Jacobi polynomials
Luc Vinet, Alexei Zhedanov
It is shown that the CMV Laurent polynomials associated to the sieved Jacobi polynomials on the unit circle satisfy an eigenvalue equation with respect to a first order differentia…
The CMV bispectrality of the Jacobi polynomials on the unit circle
Luc Vinet, Alexei Zhedanov
We show that the Jacobi polynomials that are orthogonal on the unit circle (the Jacobi OPUC) are CMV bispectral. This means that the corresponding Laurent polynomials in the CMV ba…
An algebraic treatment of the Pastro polynomials on the real line
Vutha Vichhea Chea, Luc Vinet, Meri Zaimi +1
The properties of the Pastro polynomials on the real line are studied with the help of a triplet of -difference operators. The -difference equation and recurrence relation th…
Continuous Hypergeometric Orthogonal Polynomials
Jonathan Pelletier, Luc Vinet, Alexei Zhedanov
The study of orthogonal polynomials viewed as limits of the -orthogonal polynomials is pursued. This paper present the continuous polynomials part of the analo…
biorthogonal polynomials of Hahn type
Luc Vinet, Meri Zaimi, Alexei Zhedanov
A finite family of polynomials is introduced and studied. It consists in a set of polynomials of form whose biorthogonality to an ensemble of rational functions i…