Invertebrates.—R.C. Brusca and G. J. Brusca. 2003. Sinauer Associates, Sunderland, Massachusetts. xix + 936 pp. ISBN 0–87893–097–3. $109.95(cloth).

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 $q=-1$.