Dual forms of the orthogonality relations of some classical q-orthogonal polynomials
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913590375612416 |
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| author | Chen, Qi Ma, Xinrong Wang, Jin |
| author_facet | Chen, Qi Ma, Xinrong Wang, Jin |
| contents | In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete and continuous $q$-orthogonal polynomials from the Askey-scheme such as the little and big $q$-Jacobi, $q$-Racah, (generalized) $q$-Laguerre, as well as the Askey-Wilson polynomials. As one of the most interesting results, we show that the Askey-Wilson $q$-beta integral represented in terms of the VWP-balanced $\,_8ϕ_7$ series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_13563 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dual forms of the orthogonality relations of some classical q-orthogonal polynomials Chen, Qi Ma, Xinrong Wang, Jin Combinatorics 33D15, 05A30 In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete and continuous $q$-orthogonal polynomials from the Askey-scheme such as the little and big $q$-Jacobi, $q$-Racah, (generalized) $q$-Laguerre, as well as the Askey-Wilson polynomials. As one of the most interesting results, we show that the Askey-Wilson $q$-beta integral represented in terms of the VWP-balanced $\,_8ϕ_7$ series is just a dual form of the orthogonality relation of the Askey-Wilson polynomials. |
| title | Dual forms of the orthogonality relations of some classical q-orthogonal polynomials |
| topic | Combinatorics 33D15, 05A30 |
| url | https://arxiv.org/abs/2207.13563 |