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Coefficients of Wronskian Hermite polynomials

Bonneux, Niels, Dunning, Clare, Stevens, Marco (2020) Coefficients of Wronskian Hermite polynomials. Studies in Applied Mathematics, 144 (3). pp. 245-288. ISSN 0022-2526. (doi:10.1111/sapm.12290) (KAR id:79649)


We study Wronskians of Hermite polynomials labeled by partitions and use the combinatorial concepts of cores and quotients to derive explicit expressions for their coefficients. These coefficients can be expressed in terms of the characters of irreducible representations of the symmetric group, and also in terms of hook lengths. Further, we derive the asymptotic behavior of the Wronskian Hermite polynomials when the length of the core tends to infinity, while fixing the quotient. Via this combinatorial setting, we obtain in a natural way the generalization of the correspondence between Hermite and Laguerre polynomials to Wronskian Hermite polynomials and Wronskians involving Laguerre polynomials. Lastly, we generalize most of our results to polynomials that have zeros on the p‐star

Item Type: Article
DOI/Identification number: 10.1111/sapm.12290
Uncontrolled keywords: asymptotic behavior, characters coefficients, cores and quotients, Hermite polynomials, hook ratios, Laguerre polynomials, Maya diagrams, partitions Wronskians
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Clare Dunning
Date Deposited: 21 Jan 2020 09:24 UTC
Last Modified: 08 Dec 2022 22:45 UTC
Resource URI: (The current URI for this page, for reference purposes)

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