The Askey-Wilson polynomials and q-Sturm-Liouville problems

  title={The Askey-Wilson polynomials and q-Sturm-Liouville problems},
  author={B. M. Brown and William Desmond Evans and Mourad E. H. Ismail},
We find the adjoint of the Askey–Wilson divided difference operator with respect to the inner product on L2(–1, 1, (1– x2)½dx) defined 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. 
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