Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations

Details Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations

2010-04-05

arxiv.org/abs/1004.0544v2

J.Phys.A43:335201,2010

Physics

Mathematical Physics

24 pages. Comments and references added. To appear in J.Phys.A

Scientific paper

10.1088/1751-8113/43/33/335201

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.

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