Andrea Bruder, Christian Krattenthaler and Sergei K. Suslov

An eigenvalue problem for the associated Askey-Wilson polynomials

(15 pages)

Abstract. To derive an eigenvalue problem for the associated Askey-Wilson polynomials, we consider an auxiliary function in two variables which is related to the associated Askey-Wilson polynomials introduced by Ismail and Rahman. The Askey-Wilson operator, applied in each variable separately, maps this function to the ordinary Askey-Wilson polynomials with different sets of parameters. A third Askey-Wilson operator is found with the help of a computer algebra program which links the two, and an eigenvalue problem is stated.

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The paper is accompanied by the Mathematica notebooks which allow one to derive the contiguous relations (5.5) (respectively (A.1)) and (A.2) in the article.
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