Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910493740892160 |
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| author | Odake, Satoru |
| author_facet | Odake, Satoru |
| contents | The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, $q$-Racah, big $q$-Jacobi etc.) and they are related to the factorization of the differential or difference operators. Based on other factorizations, we obtain another type of forward and backward shift relations. Essentially, these shift relations shift only the parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00678 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme Odake, Satoru Classical Analysis and ODEs High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, $q$-Racah, big $q$-Jacobi etc.) and they are related to the factorization of the differential or difference operators. Based on other factorizations, we obtain another type of forward and backward shift relations. Essentially, these shift relations shift only the parameters. |
| title | Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme |
| topic | Classical Analysis and ODEs High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2301.00678 |