  We have investigated S-wave bound states composed of three identical bosons
interacting via regulated delta function potentials in non-relativistic quantum
mechanics. For low-energy systems, these short-range potentials serve as an
approximation to the underlying physics, leading to an effective field theory.
  A method for perturbatively expanding the three-body bound-state equation in
inverse powers of the cutoff is developed. This allows us to extract some
analytical results concerning the behavior of the system. Further results are
obtained by solving the leading order equations numerically to 11 or 12 digits
of accuracy. The limit-cycle behavior of the required three-body contact
interaction is computed, and the cutoff-independence of bound-state energies is
shown. By studying the relationship between the two- and three-body binding
energies, we obtain a high accuracy numerical calculation of Efimov's universal
function.
  Equations for the first order corrections, necessary for the study of cutoff
dependence, are derived. However, a numerical solution of these equations is
not attempted.
