A "missing" family of classical orthogonal polynomials

Details A "missing" family of classical orthogonal polynomials A "missing" family of classical orthogonal polynomials

2010-11-07

arxiv.org/abs/1011.1669v3

J. Phys. A: Math. Theor. v.44 (2011), 085201

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

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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