Geodesic
Para-Bannai–Ito Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 complementary Bannai–Ito polynomials. A complete characterization of the resulting para-Bannai–Ito polynomials is provided, including a three term recurrence relation, a Dunkl-difference equation, an explicit expression in terms of hypergeometric series and an orthogonality relation. They are also derived as a $q\to -1$ limit of the $q$-para-Racah polynomials. A connection to the dual $-1$ Hahn polynomials is also established.
Keywords: Dunkl operators.
Mots-clés : para-orthogonal polynomials, Bannai–Ito polynomials 
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     author = {Jonathan Pelletier and Luc Vinet and Alexei Zhedanov},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a89/}
}
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Jonathan Pelletier; Luc Vinet; Alexei Zhedanov. Para-Bannai–Ito Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a89/

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