Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914766536048640 |
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| author | Branquinho, Amílcar Díaz, Juan EF Foulquié-Moreno, Ana Mañas, Manuel |
| author_facet | Branquinho, Amílcar Díaz, Juan EF Foulquié-Moreno, Ana Mañas, Manuel |
| contents | This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation Branquinho, Amílcar Díaz, Juan EF Foulquié-Moreno, Ana Mañas, Manuel Classical Analysis and ODEs Mathematical Physics 42C05, 33C45, 33C47, 47B39, 47B36 This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials. |
| title | Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation |
| topic | Classical Analysis and ODEs Mathematical Physics 42C05, 33C45, 33C47, 47B39, 47B36 |
| url | https://arxiv.org/abs/2404.13958 |