The Askey - Wilson Polynomials and q - Sturm - Liouville Problems

Abstract

We nd the adjoint of the Askey-Wilson divided di erence operator with respect to the inner product on L 2 ( 1; 1; (1 x 2 ) 1=2 dx) de ned as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator. Running title: q-Sturm-Liouville Problems. 1990 Mathematics Subject Classi cation: Primary 33D45, Secondary 47B39.

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Cite this paper

@inproceedings{Ismail1996TheA, title={The Askey - Wilson Polynomials and q - Sturm - Liouville Problems}, author={Mourad E. H. Ismail}, year={1996} }