## 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.

The following versions are available:

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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