-Hypergeometric Orthogonal Polynomials with = −1
We obtain some properties of a class of -hypergeometric orthogonal polynomials with = −1, described by a uniform parametrization of the recurrence coefficients. We construct a class of complementary −1 polynomials by means of the Darboux transformation with a shift. We show that our classes conta...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214203 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | -Hypergeometric Orthogonal Polynomials with = −1. Luis Verde-Star. SIGMA 21 (2025), 083, 19 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862615479888117760 |
|---|---|
| author | Verde-Star, Luis |
| author_facet | Verde-Star, Luis |
| citation_txt | -Hypergeometric Orthogonal Polynomials with = −1. Luis Verde-Star. SIGMA 21 (2025), 083, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We obtain some properties of a class of -hypergeometric orthogonal polynomials with = −1, described by a uniform parametrization of the recurrence coefficients. We construct a class of complementary −1 polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials, their complementary polynomials, and other known −1 polynomials. We introduce some new examples of −1 polynomials and also obtain matrix realizations of the Bannai-Ito algebra.
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| first_indexed | 2026-03-21T12:22:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214203 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:22:35Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Verde-Star, Luis 2026-02-20T08:04:16Z 2025 -Hypergeometric Orthogonal Polynomials with = −1. Luis Verde-Star. SIGMA 21 (2025), 083, 19 pages 1815-0659 2020 Mathematics Subject Classification: 33C45; 33D45 arXiv:2410.14068 https://nasplib.isofts.kiev.ua/handle/123456789/214203 https://doi.org/10.3842/SIGMA.2025.083 We obtain some properties of a class of -hypergeometric orthogonal polynomials with = −1, described by a uniform parametrization of the recurrence coefficients. We construct a class of complementary −1 polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials, their complementary polynomials, and other known −1 polynomials. We introduce some new examples of −1 polynomials and also obtain matrix realizations of the Bannai-Ito algebra. I am very grateful to the anonymous referees for their many suggestions, which helped improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications -Hypergeometric Orthogonal Polynomials with = −1 Article published earlier |
| spellingShingle | -Hypergeometric Orthogonal Polynomials with = −1 Verde-Star, Luis |
| title | -Hypergeometric Orthogonal Polynomials with = −1 |
| title_full | -Hypergeometric Orthogonal Polynomials with = −1 |
| title_fullStr | -Hypergeometric Orthogonal Polynomials with = −1 |
| title_full_unstemmed | -Hypergeometric Orthogonal Polynomials with = −1 |
| title_short | -Hypergeometric Orthogonal Polynomials with = −1 |
| title_sort | -hypergeometric orthogonal polynomials with = −1 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214203 |
| work_keys_str_mv | AT verdestarluis hypergeometricorthogonalpolynomialswith1 |