e-mail: masson@math.toronto.edu

**Indeterminate Cases within the Askey-Wilson Scheme**

**Abstract**

The orthogonal polynomials associated with an indeterminate moment problem
have infinitely many measures of orthogonality. The one parameter family
of $N$-extremal measures $\sigma(x,\lambda)$ are discribed in terms of
four entire functions $A(z)$, $B(z)$, $C(z)$ and $D(z)$ by $$\int \frac{d\sigma(x,\lambda)}{z-x}=(A(z)-\lambda
C(z))/ (B(z)-\lambda D(z)), \qquad \lambda \in R.$$

The Askey-Wilson polynomials are described in terms of four parameters
$a$, $b$, $c$, $d$. We take a limit when one parameter, say $d$, tends
to infinity to obtain a new family of orthogonal polynomials associated
with an indeterminate case. We show how to obtain explicit expression for
the corresponding entire functions $A(z)$, $B(z)$, $C(z)$ , $D(z)$ in terms
of $q$-hypergeometric functions.