An evolution of matrix-valued orthogonal polynomials
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915463918780416 |
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| author | Koelink, Erik Román, Pablo Zudilin, Wadim |
| author_facet | Koelink, Erik Román, Pablo Zudilin, Wadim |
| contents | We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating functions, distribution of zeros for individual entries of the matrices and new type of differential-difference structure. We further speculate about other potentials of the connection formulas found. Part of our proofs makes use of creative telescoping in a matrix setting$-$the strategy which is not yet developed algorithmically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An evolution of matrix-valued orthogonal polynomials Koelink, Erik Román, Pablo Zudilin, Wadim Classical Analysis and ODEs Mathematical Physics Combinatorics Number Theory Representation Theory 33C45, 33C47, 33E30, 33F10 We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating functions, distribution of zeros for individual entries of the matrices and new type of differential-difference structure. We further speculate about other potentials of the connection formulas found. Part of our proofs makes use of creative telescoping in a matrix setting$-$the strategy which is not yet developed algorithmically. |
| title | An evolution of matrix-valued orthogonal polynomials |
| topic | Classical Analysis and ODEs Mathematical Physics Combinatorics Number Theory Representation Theory 33C45, 33C47, 33E30, 33F10 |
| url | https://arxiv.org/abs/2411.18362 |