  We consider the evolution of the one-particle function in the weak-coupling
limit in three space dimensions, obtained by truncating the BBGKY hierarchy
under a propagation of chaos approximation. For this dynamics, we rigorously
show the convergence to a solution of the Landau equation, keeping the full
singularity of the Landau kernel. This resolves the issue arising from [10],
where the singular region has been removed artificially. Since the singularity
appears in the Landau equation due to the geometry of particle interactions, it
is an intrinsic physical property of the weak-coupling limit which is crucial
to the understanding of the transition from particle systems to the Landau
equation.
