  We first introduce and derive some basic properties of a two-parameters
family of one-sided Levy processes. Their Laplace exponents are given in terms
of the Pochhammer symbol. This family includes, in a limit case, the family of
Brownian motion with drifts. Then, we proceed by computing the density of the
law of the exponential functional associated to some elements of this family
(and their dual) and some transformations of these elements. These densities
are expressed in terms of the Wright hypergeometric functions. By means of
probabilistic arguments, we derive some interesting properties enjoyed by these
functions. On the way we also characterize explicitly the density of the
semi-groups of the family of self-similar continuous state branching processes
with immigration.
