  There are two families of Donaldson invariants for the complex projective
plane, corresponding to the SU(2)-gauge theory and the SO(3)-gauge theory with
non-trivial Stiefel-Whitney class. In 1997 Moore and Witten conjectured that
the regularized u-plane integral on the complex projective plane gives the
generating functions for these invariants. In earlier work the second two
authors proved the conjecture for the SO(3)-gauge theory. Here we complete the
proof of the conjecture by confirming the claim for the SU(2)-gauge theory. As
a consequence, we find that the SU(2) Donaldson invariants for CP^2 are
explicit linear combinations of the Hurwitz class numbers which arise in the
theory of imaginary quadratic fields and orders.
