Recurrence relations for exceptional Hermite polynomials.
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2016
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Academic Press-Elsevier Science
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Abstract
The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as eigenfunctions with eigenvalues that are polynomials in x.
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© 2015 Elsevier Inc. All rights reserved.
The authors are grateful to the organizers of the conference NEEDS 2015 in Sardinia, Italy without which we might never have recognized the potential application of these tools to this problem. Likewise, the authors are grateful to Yves Grandati and Satoshi Tsujimoto for helpful conversations and their presentations on related topics at that conference.
D.G.U. has been supported in part by Spanish MINECO Grants MTM2012-31714 and FIS2012-38949-C03-01 and by the ICMAT-Severo Ochoa grant SEV-2011-0087. A.B.J.K. is supported by KU Leuven Research Grant OT/12/073, the Belgian Interuniversity Attraction Pole P07/18, and FWO Flanders projects G.0641.11, G.0934.13, G.0864.16. R.M. is supported by NSERC grant RGPIN-228057-2004.