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Wronskian Appell polynomials and symmetric functions

Journal Contribution - Journal Article

We study Wronskians of Appell polynomials indexed by integer partitions. These families of polynomials appear in rational solutions of certain Painlevé equations and in the study of exceptional orthogonal polynomials. We determine their derivatives, their average and variance with respect to Plancherel measure, and introduce several recurrence relations. In addition, we prove an integrality conjecture for Wronskian Hermite polynomials previously made by the first and last authors. Our proofs all exploit strong connections with the theory of symmetric functions.
Journal: Advances in Applied Mathematics
ISSN: 0196-8858
Issue: October 2019
Volume: 111
Publication year:2019
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:1
CSS-citation score:2
Authors:International
Authors from:Higher Education
Accessibility:Closed