  We provide an analytic solution for the mean-field equations and for the
relevant physical quantities at the Gaussian level, in terms of the complete
elliptic integrals of the first and second kinds, for the crossover problem
from BCS superconductivity to Bose-Einstein condensation of a three-dimensional
system of free fermions interacting via an attractive contact potential at zero
temperature. This analytic solution enables us to follow the evolution between
the two limits in a particularly simple and transparent way, as well as to
verify the absence of singularities during the evolution.
