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The Heun operator of Hahn-type

Authors: Luc Vinet and Alexei Zhedanov
Journal: Proc. Amer. Math. Soc. 147 (2019), 2987-2998
MSC (2010): Primary 33C45, 33C80, 39A70
Published electronically: March 7, 2019
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Abstract: The Heun-Hahn operator on the uniform grid is defined. This operator is shown to map polynomials of degree $ n$ to polynomials of degree $ n+1$, to be tridiagonal in bases made out of either Pochhammer or Hahn polynomials, and to be bilinear in the operators of the Hahn algebra. The extension of this algebra that includes the Heun-Hahn operator as generator is described. Biorthogonal rational functions on uniform grids are shown to be related to this framework.

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Additional Information

Luc Vinet
Affiliation: Centre de recherches mathématiques, Université de Montréal, P.O. Box 6128, Centreville Station, Montréal, Québec, H3C 3J7 Canada

Alexei Zhedanov
Affiliation: Department of Mathematics, School of Information, Renmin University of China, Beijing 100872, People’s Republic of China

Received by editor(s): July 17, 2018
Received by editor(s) in revised form: October 10, 2018
Published electronically: March 7, 2019
Additional Notes: The research of the first author was funded in part by a discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.
The work of the second author was supported by the National Science Foundation of China (Grant No.11771015).
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society