Para-Bannai-Ito Polynomials
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, inclu...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212041 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Para-Bannai-Ito Polynomials. Jonathan Pelletier, Luc Vinet and Alexei Zhedanov. SIGMA 19 (2023), 090, 19 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 → −1 limit of the -para-Racah polynomials. A connection to the dual −1 Hahn polynomials is also established.
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| ISSN: | 1815-0659 |