Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915903646466048 |
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| author | Odake, Satoru |
| author_facet | Odake, Satoru |
| contents | We present the case-(1) multi-indexed orthogonal polynomials of a discrete variable for 8 types ((dual)($q$-)Hahn, three kinds of $q$-Krawtchouk and $q$-Meixner). Based on them and the case-(1) multi-indexed orthogonal polynomials of Racah, $q$-Racah, Meixner, little $q$-Jacobi and little $q$-Laguerre types, exactly solvable continuous time birth and death processes are obtained. Their discrete time versions (Markov chains) are also obtained for finite types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes Odake, Satoru Mathematical Physics High Energy Physics - Theory Classical Analysis and ODEs Probability We present the case-(1) multi-indexed orthogonal polynomials of a discrete variable for 8 types ((dual)($q$-)Hahn, three kinds of $q$-Krawtchouk and $q$-Meixner). Based on them and the case-(1) multi-indexed orthogonal polynomials of Racah, $q$-Racah, Meixner, little $q$-Jacobi and little $q$-Laguerre types, exactly solvable continuous time birth and death processes are obtained. Their discrete time versions (Markov chains) are also obtained for finite types. |
| title | Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes |
| topic | Mathematical Physics High Energy Physics - Theory Classical Analysis and ODEs Probability |
| url | https://arxiv.org/abs/2501.02877 |