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An evolution of
matrix-valued orthogonal polynomials
Erik Koelink, Pablo Román and Wadim Zudilin |
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Vol. 338 (2025), No. 2, 325–348
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Abstract |
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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. |
Keywords
experimental mathematics, orthogonal polynomials,
matrix-valued polynomials, differential-difference
operators, zeros of polynomials, creative telescoping
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Mathematical Subject Classification
Primary: 33C45
Secondary: 33C47, 33E30, 33F10
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Milestones
Received: 6 December 2024
Revised: 2 July 2025
Accepted: 4 July 2025
Published: 24 August 2025
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Authors |
| Erik Koelink | |
| IMAPP Radboud University Nijmegen Netherlands |
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| Pablo Román | |
| FaMAF-CIEM Universidad Nacional de Córdoba Córdoba Argentina |
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| Wadim Zudilin | |
| IMAPP Radboud University Nijmegen Netherlands |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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