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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…
Para-Bannai-Ito Polynomials
Jonathan Pelletier, Luc Vinet, Alexei Zhedanov
New bispectral polynomials orthogonal on a Bannai-Ito bi-lattice (uniform quadri-lattice) are obtained from an unconventional truncation of the untruncated Bannai-Ito and complemen…
Bispectrality and biorthogonality of the rational functions of -Hahn type
Ismaël Bussière, Julien Gaboriaud, Luc Vinet +1
We introduce families of rational functions that are biorthogonal with respect to the -hypergeometric distribution. A triplet of -difference operators , , is shown…
The single-indexed exceptional Krawtchouk polynomials
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
The Darboux transformations of Krawtchouk polynomials are investigated and all possible exceptional Krawtchouk polynomials obtainable from a single-step Darboux transformation are…