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A "missing" family of classical orthogonal polynomials

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arxiv 1011.1669 v3 pith:ZNH3Q6AK submitted 2010-11-07 math.CA

classification math.CA
keywords polynomialsclassicalfamilyorthogonalalgebraapartaskey-wilsondifferential
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abstract

We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q=-1$.

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