  In an earlier paper (hep-th/0101127), we developed heat kernel techniques in
N = 2 harmonic superspace for the calculation of the low-energy effective
action of N = 4 SYM theory, which can be considered as the most symmetric N = 2
SYM theory. Here, the results are extended to generic N = 2 SYM theories. This
involves a prescription for computing the variation of the hypermultiplet
effective action. Integrability of this variation allows the hypermultiplet
effective action to be deduced. This prescription permits a very simple
superfield derivation of the perturbative holomorphic prepotential. Explicit
calculations of the prepotential and the leading non-holomorphic correction are
presented.
