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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02032 |
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| _version_ | 1866916879187050496 |
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| author | Huang, Hau-Wen |
| author_facet | Huang, Hau-Wen |
| contents | The dual Hahn polynomials $\{u_i(x)\}_{i=0}^d$ are a family of discrete orthogonal polynomials involving two real parameters $r$ and $s$. Let $L,L^*$ denote the corresponding Leonard pair. Assume that $r\not=0$ and $r+s=0$. We show that $L,(L^*+\frac{r-d}{2})^{2}$ is a Leonard pair. According to the theory of Leonard pairs, the polynomials $\{u_i(x)\}_{i=0}^d$ are not only the dual Hahn polynomials but also the Racah polynomials with respect to the same inner product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A way to treat dual Hahn polynomials as Racah polynomials via the theory of Leonard pairs Huang, Hau-Wen Classical Analysis and ODEs Combinatorics 05E30, 16S30, 33C45 The dual Hahn polynomials $\{u_i(x)\}_{i=0}^d$ are a family of discrete orthogonal polynomials involving two real parameters $r$ and $s$. Let $L,L^*$ denote the corresponding Leonard pair. Assume that $r\not=0$ and $r+s=0$. We show that $L,(L^*+\frac{r-d}{2})^{2}$ is a Leonard pair. According to the theory of Leonard pairs, the polynomials $\{u_i(x)\}_{i=0}^d$ are not only the dual Hahn polynomials but also the Racah polynomials with respect to the same inner product. |
| title | A way to treat dual Hahn polynomials as Racah polynomials via the theory of Leonard pairs |
| topic | Classical Analysis and ODEs Combinatorics 05E30, 16S30, 33C45 |
| url | https://arxiv.org/abs/2508.02032 |