  We study Coulomb branch (``u-plane'') integrals for $\mathcal{N}=2$
supersymmetric $SU(2),SO(3)$ Yang-Mills theory on 4-manifolds $X$ of $b_1(X)>0,
b_2^+(X)=1$. Using wall-crossing arguments we derive expressions for the
Donaldson invariants for manifolds with $b_1(X)>0, b_2^+(X)>0$. Explicit
expressions for $X=\IC P^1 \times F_g$, where $F_g$ is a Riemann surface of
genus $g$ are obtained using Kronecker's double series identity. The result
might be useful in future studies of quantum cohomology.
