INSTANTONS AND RECURSION RELATIONS IN N=2 SUSY GAUGE THEORY

We find the transformation properties of the prepotential F of N = 2 SUSY gauge theory with gauge group SU(2). Next we show that G(a) = \u3c0i(F(a) -1/2a 02aF(a)) is modular invariant. We also show that u = G(a), so that F() =1/\u3c0i + 1/2. This implies thatG (a) satisfies the non-linear differential equation (1 - G2) G'' +1/4aG '3 = 0. We use this equation to derive recursion relations for the instanton contributions. These results can be extended to more general cases