Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
Mathematical Physics
2011-03-28 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum transformations intertwining the discrete quantum mechanical systems of the original and the exceptional polynomials play an important role. Infinitely many continuous Hahn polynomials are derived in the same manner. The present method provides a simple proof of the shape invariance of these systems as in the corresponding cases of the exceptional Laguerre and Jacobi polynomials.
Cite
@article{arxiv.1004.0544,
title = {Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1004.0544},
year = {2011}
}
Comments
24 pages. Comments and references added. To appear in J.Phys.A