  We calculate moments and moment generating functions of two distributions:
the so called $q-$Normal and the so called conditional $q-$Normal
distributions. These distributions generalize both Normal ($q=1),$ Wigner ($%
q=0,$ $q-$Normal) and Kesten-McKay ($q=0,$ conditional $q-$Normal)
distributions. As a by product we get asymptotic properties of some expansions
in modified Bessel functions.
