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arXiv · 1011.1669

A "missing" family of classical orthogonal polynomials

Luc Vinet·Alexei Zhedanov
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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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Luc Vinet, Alexei Zhedanov. 2010-11-07. A "missing" family of classical orthogonal polynomials. https://doi.org/10.1088/1751-8113/44/8/085201

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