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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | 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 |
| Цитувати: | Para-Bannai-Ito Polynomials. Jonathan Pelletier, Luc Vinet and Alexei Zhedanov. SIGMA 19 (2023), 090, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862658390190194688 |
|---|---|
| author | Pelletier, Jonathan Vinet, Luc Zhedanov, Alexei |
| author_facet | Pelletier, Jonathan Vinet, Luc Zhedanov, Alexei |
| citation_txt | Para-Bannai-Ito Polynomials. Jonathan Pelletier, Luc Vinet and Alexei Zhedanov. SIGMA 19 (2023), 090, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-16T00:26:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212041 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T00:26:00Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Pelletier, Jonathan Vinet, Luc Zhedanov, Alexei 2026-01-23T10:10:51Z 2023 Para-Bannai-Ito Polynomials. Jonathan Pelletier, Luc Vinet and Alexei Zhedanov. SIGMA 19 (2023), 090, 19 pages 1815-0659 2020 Mathematics Subject Classification: 33C45 arXiv:2209.10725 https://nasplib.isofts.kiev.ua/handle/123456789/212041 https://doi.org/10.3842/SIGMA.2023.090 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. JP holds a scholarship from Fonds de recherche Québécois – nature et technologies (FRQNT) and an academic excellence scholarship from Hydro-Québec. The research of LV is supported in part by a Discovery grant from the Natural Science and Engineering Research Council (NSERC) of Canada. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Para-Bannai-Ito Polynomials Article published earlier |
| spellingShingle | Para-Bannai-Ito Polynomials Pelletier, Jonathan Vinet, Luc Zhedanov, Alexei |
| title | Para-Bannai-Ito Polynomials |
| title_full | Para-Bannai-Ito Polynomials |
| title_fullStr | Para-Bannai-Ito Polynomials |
| title_full_unstemmed | Para-Bannai-Ito Polynomials |
| title_short | Para-Bannai-Ito Polynomials |
| title_sort | para-bannai-ito polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212041 |
| work_keys_str_mv | AT pelletierjonathan parabannaiitopolynomials AT vinetluc parabannaiitopolynomials AT zhedanovalexei parabannaiitopolynomials |