  We consider four-dimensional Omega-deformed N=2 supersymmetric SU(2) gauge
theory on A1 space and its lift to five dimensions. We find that the partition
functions can be reproduced via special geometry and the holomorphic anomaly
equation. Schwinger type integral expressions for the boundary conditions at
the monopole/dyon point in moduli space are inferred. The interpretation of the
five-dimensional partition function as the partition function of a refined
topological string on A1x(local P1xP1) is suggested.
