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1 - Exceptional Orthogonal Polynomials via Krall Discrete Polynomials

Published online by Cambridge University Press:  07 October 2020

By
Antonio J. Durán
Edited by
Howard S. Cohl  and
Mourad E. H. Ismail
Howard S. Cohl
Affiliation:
National Institute of Standards and Technology
Mourad E. H. Ismail
Affiliation:
University of Central Florida
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Summary

We consider two important extensions of the classical and classical discrete orthogonal polynomials: namely, Krall and exceptional polynomials. We also explore the relationship between both extensions and how they can be used to expand the Askey tableau.

Keywords

orthogonal polynomialsKrall and discrete polynomialsexceptional and exceptional discrete polynomialsD-operatorsAskey tableauKrall–Charlier polynomialsKrall–Laguerre polynomialsexceptional Charlier polynomialsexceptional Hermite polynomialsexceptional Laguerre polynomials
Type
Chapter
Information
Lectures on Orthogonal Polynomials and Special Functions , pp. 1 - 75
Publisher: Cambridge University Press
Print publication year: 2020

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