Algebras behind the bispectrality of the Wilson rational functions and their ${}_4ϕ_3$ limits
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909901248266240 |
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| author | Crampe, Nicolas Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei |
| author_facet | Crampe, Nicolas Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei |
| contents | The properties of the Wilson rational functions ${}_{10}ϕ_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a generalized eigenvalue problem. The so-called Wilson rational algebra is introduced, which encodes algebraically the spectral properties of these special functions. Finally, different limits are considered, leading up to functions proportional to ${}_{4}ϕ_3$. For one of these, the spectral algebra simplifies to yield the meta $q$-Racah algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebras behind the bispectrality of the Wilson rational functions and their ${}_4ϕ_3$ limits Crampe, Nicolas Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei Mathematical Physics The properties of the Wilson rational functions ${}_{10}ϕ_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a generalized eigenvalue problem. The so-called Wilson rational algebra is introduced, which encodes algebraically the spectral properties of these special functions. Finally, different limits are considered, leading up to functions proportional to ${}_{4}ϕ_3$. For one of these, the spectral algebra simplifies to yield the meta $q$-Racah algebra. |
| title | Algebras behind the bispectrality of the Wilson rational functions and their ${}_4ϕ_3$ limits |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2502.04275 |