A "missing" family of classical orthogonal polynomials

Luc Vinet, Alexei Zhedanov

Published 2010-11-07, updated 2011-11-20Version 3

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 $q=-1$.