  Laurent polynomials related to the Hahn-Exton $q$-Bessel function, which are
$q$-analogues of the Lommel polynomials, have been introduced by Koelink and
Swarttouw. The explicit strong moment functional with respect to which the
Laurent $q$-Lommel polynomials are orthogonal is given. The strong moment
functional gives rise to two positive definite moment functionals. For the
corresponding sets of orthogonal polynomials the orthogonality measure is
determined using the three-term recurrence relation as a starting point. The
relation between Chebyshev polynomials of the second kind and the Laurent
$q$-Lommel polynomials and related functions is used to obtain estimates for
the latter.
