Griffiths polynomials of Racah type
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914977159315456 |
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| author | Crampe, Nicolas Frappat, Luc Gaboriaud, Julien Ragoucy, Eric Vinet, Luc Zaimi, Meri |
| author_facet | Crampe, Nicolas Frappat, Luc Gaboriaud, Julien Ragoucy, Eric Vinet, Luc Zaimi, Meri |
| contents | Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indices and variables of these polynomials is also determined. Particular limits on the parameters entering the polynomials allow to define several Griffiths polynomials of other types. One special limit connects them to the original Griffiths polynomials (of Krawtchouk type). Finally, a connection with the $9j$ symbols is made. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Griffiths polynomials of Racah type Crampe, Nicolas Frappat, Luc Gaboriaud, Julien Ragoucy, Eric Vinet, Luc Zaimi, Meri Mathematical Physics 33C80, 33C45, 16G60 Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indices and variables of these polynomials is also determined. Particular limits on the parameters entering the polynomials allow to define several Griffiths polynomials of other types. One special limit connects them to the original Griffiths polynomials (of Krawtchouk type). Finally, a connection with the $9j$ symbols is made. |
| title | Griffiths polynomials of Racah type |
| topic | Mathematical Physics 33C80, 33C45, 16G60 |
| url | https://arxiv.org/abs/2403.12148 |