  We study two families of orthogonal polynomials. The first is a finite family
related to the Askey-Wilson polynomials but the orthogonality is on the real
line. A limiting case of this family is an infinite system of orthogonal
polynomials whose moment problem is indeterminate. We provide several
orthogonality measures for the infinite family and derive their
Plancherel-Rotach asymptotics.
