  We have studied the numerical solutions of Richardson equations of the BCS
model in the limit of large number of energy levels at half-filling, and
compare them with the analytic results derived by Gaudin and Richardson, which
in turn leads to the standard BCS solution. We focus on the location and
density of the roots, the eigenvalues of the conserved quantities, and the
scaling properties of the total energy for the equally spaced and the two-level
models.
