Contiguity relations for finite families of orthogonal polynomials in the Askey scheme
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918004374110208 |
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| author | Crampé, Nicolas Morey, Lucia Vinet, Luc Zaimi, Meri |
| author_facet | Crampé, Nicolas Morey, Lucia Vinet, Luc Zaimi, Meri |
| contents | This paper classifies the contiguity relations for finite families of polynomials within the ($q$-)Askey scheme. The necessary and sufficient conditions for the existence of these contiguity relations are presented first. These conditions are then solved, yielding a comprehensive list of contiguity relations for these various families of polynomials. Furthermore, we demonstrate that all contiguity relations correspond to spectral transforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contiguity relations for finite families of orthogonal polynomials in the Askey scheme Crampé, Nicolas Morey, Lucia Vinet, Luc Zaimi, Meri Classical Analysis and ODEs 33C80, 33C45, 16G60 This paper classifies the contiguity relations for finite families of polynomials within the ($q$-)Askey scheme. The necessary and sufficient conditions for the existence of these contiguity relations are presented first. These conditions are then solved, yielding a comprehensive list of contiguity relations for these various families of polynomials. Furthermore, we demonstrate that all contiguity relations correspond to spectral transforms. |
| title | Contiguity relations for finite families of orthogonal polynomials in the Askey scheme |
| topic | Classical Analysis and ODEs 33C80, 33C45, 16G60 |
| url | https://arxiv.org/abs/2504.20802 |