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

DOI:
https://doi.org/10.1090/proc/14425

Published electronically:
March 7, 2019

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Abstract | References | Similar Articles | Additional Information

Abstract: The Heun-Hahn operator on the uniform grid is defined. This operator is shown to map polynomials of degree to polynomials of degree , 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

DOI:
https://doi.org/10.1090/proc/14425

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