  Using a recently developed approach for solving the three dimensional Dirac
equation with spherical symmetry, we obtain simple representations for the
Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is
accomplished by setting up the relativistic problem in such a way that makes
comparison with the nonrelativistic problem highly transparent and results in a
map of the latter into the former. An advantage of this representation is in
the computational economy as depicted by the number of terms, which are
quadratic in the Whittaker functions. These are single terms except for the
off-diagonal elements of the Dirac-Coulomb Green's function which, nonetheless,
simplifies into the sum of a first order and third order relativistic terms.
