-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 |
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| 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| Summary: | 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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| ISSN: | 1815-0659 |