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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.00261 |
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| _version_ | 1866914180578148352 |
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| author | Koelink, Erik Román, Pablo Zudilin, Wadim |
| author_facet | Koelink, Erik Román, Pablo Zudilin, Wadim |
| contents | There are several questions one may ask about polynomials $q_m(x)=q_m(x;t)=\sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal polynomials $\{p_n(x)\}_{n\ge0}$. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of $q_m(x;t)$ in the case of varying real parameter $t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A partial-sum deformation for a family of orthogonal polynomials Koelink, Erik Román, Pablo Zudilin, Wadim Classical Analysis and ODEs There are several questions one may ask about polynomials $q_m(x)=q_m(x;t)=\sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal polynomials $\{p_n(x)\}_{n\ge0}$. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of $q_m(x;t)$ in the case of varying real parameter $t$. |
| title | A partial-sum deformation for a family of orthogonal polynomials |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2409.00261 |