  We consider the Faddeev-Green function in the three-dimensional space and in
a slab, and we construct formal asymptotic expansions for the large complex
parameter appearing in this function. The basic idea of the construction is to
express the Faddeev-Green function through the standard exponential integral
and to use the standard asymptotic expansion of this special function. In the
three-dimensional space, the constructed expansion of the Faddeev-Green
function clearly suggests the form of the rigorous estimate proved by Sylvester
and Uhlmann. and which is the basis of complex-geometric optics' techniques in
inverse problems. A similar estimate is suggested for the slab case
