  We present a description of the behavior of a superfluid gas of fermions in
the presence of a Feshbach resonance over the complete range of magnetic field
detunings. Starting from a resonance Hamiltonian, we exploit a functional
method to describe the continuous behavior from Bardeen-Cooper-Schrieffer to
Bose-Einstein condensation type superfluidity. Our results show an ability for
a resonance system to exhibit a high critical temperature comparable to the
Fermi temperature. The results are derived in a manner that is shown to be
consistent with the underlying microscopic scattering physics.
