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arxiv: 1011.1669 · v3 · pith:ZNH3Q6AKnew · submitted 2010-11-07 · 🧮 math.CA

A "missing" family of classical orthogonal polynomials

classification 🧮 math.CA
keywords polynomialsclassicalfamilyorthogonalalgebraapartaskey-wilsondifferential
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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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