  For the Bessel function \begin{equation} \label{bessel} J_{\nu}(z) =
\sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{\nu+2k}}{k!
\Gamma(\nu+1+k)} \end{equation} there exist several $q$-analogues. The oldest
$q$-analogues of the Bessel function were introduced by F. H. Jackson at the
beginning of this century, see M. E. H. Ismail \cite{Is1} for the appropriate
references. Another $q$-analogue of the Bessel function has been introduced by
W. Hahn in a special case and by H. Exton in full generality, see R. F.
Swarttouw \cite{Sw1} for a historic overview.
  Here we concentrate on properties of the Hahn-Exton $q$-Bessel function and
in particular on its zeros and the associated $q$-Lommel polynomials.
