$q$-Hypergeometric Orthogonal Polynomials with $q=-1$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911188127842304 |
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| author | Verde-Star, Luis |
| author_facet | Verde-Star, Luis |
| contents | We obtain some properties of a class $\mathcal{A}$ of $q$-hypergeometric orthogonal polynomials with $q=-1$, described by a uniform parametrization of the recurrence coefficients. We construct a class $\mathcal{C}$ of complementary $-1$ polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials and 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_14068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $q$-Hypergeometric Orthogonal Polynomials with $q=-1$ Verde-Star, Luis Classical Analysis and ODEs 33C45, 33D45 We obtain some properties of a class $\mathcal{A}$ of $q$-hypergeometric orthogonal polynomials with $q=-1$, described by a uniform parametrization of the recurrence coefficients. We construct a class $\mathcal{C}$ of complementary $-1$ polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials and 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. |
| title | $q$-Hypergeometric Orthogonal Polynomials with $q=-1$ |
| topic | Classical Analysis and ODEs 33C45, 33D45 |
| url | https://arxiv.org/abs/2410.14068 |