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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