  We give an alternative proof of the completeness of the Chandrasekhar ansatz
for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an
integral representation for smooth compactly supported functions which in turn
we use to derive an integral representation for the propagator of solutions of
the Cauchy problem with initial data in the above class of functions. As a
by-product, we also obtain the propagator for the Dirac equation in the
Minkowski space-time in oblate spheroidal coordinates.
