  In scattering by singular potentials $g^2U(s;r)$, the coupling constant $g^2$
is continuously decreased to zero while the stage $s$ of singularity raised
simultaneously beyond all limits by some functional relation $F(g^2;s)=0$. In
the extreme situation of this double limit, even the mere existence of a
nontrivial physical scattering problem is questionable. By iterating a pair of
integral equations, the relevant solution is developed here in terms of wave
functions into a pair of convergent series, each of which reduces in the double
limit $\{g^2\to 0;s\to\infty\}$ to a single term calculable by quadrature.
