  Starting with a given generalized boson algebra U_<q>(h(1)) known as the
bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ
the Hopf duality arguments to provide the dually conjugate function algebra
Fun_<q>(H(1)). Both the Hopf algebras being finitely generated, we produce a
closed form expression of the universal T matrix that caps the duality and
generalizes the familiar exponential map relating a Lie algebra with its
corresponding group. Subsequently, using an inverse Mellin transform approach,
the coherent states of single-node systems subject to the U_<q>(h(1)) symmetry
are found to be complete with a positive-definite integration measure.
Nonclassical coalgebraic structure of the U_<q>(h(1)) algebra is found to
generate naturally entangled coherent states in bipartite composite systems.
