Conference abstracts

Session C7 - Special Functions and Orthogonal Polynomials

July 18, 14:30 ~ 15:00 - Room B5

Equivalences and recurrence formulas for exceptional orthogonal polynomials

David Gomez-Ullate

ICMAT and Universidad Complutense de Madrid, Spain   -   david.gomez-ullate@icmat.es

We will cover two recent results associated to exceptional orthogonal polynomials and Darboux transformations. The first one [1] concerns an equivalence notion of iterated Darboux transformations, that has a nice combinatorial interpretation in terms of generalized Durfee symbols and Frobenius representations of partitions and produces novel identities among Wronskians of classical orthogonal polynomals. The second one [2] refers to the structure of the higher order recurrence relations of exceptional orthogonal polynomials, derived through a bispectral isomorphism. We will comment among the similarities between the dual construction of Darboux transformations of the Jacobi matrix leading to Krall polynomials.

[1] D Gomez-Ullate, Y Grandati, R Milson, Durfee rectangles and pseudo-Wronskian equivalences for Hermite polynomials, arXiv:1612.05514

[2] D Gomez-Ullate, A Kasman, ABJ Kuijlaars, R Milson, Recurrence relations for exceptional Hermite polynomials, J. Approx. Theory 204 (2016) 1-16

Joint work with Yves Grandati (Université de Metz), Robert Milson (Dalhousie University), Alex Kasman (Charleston College) and Arno Kuijlaars (KU Leuven).

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