Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets

We compute instanton corrections to the low energy effective prepotential of N=2 supersymmetric theories in a variety of cases, including all classical gauge groups and even number of fundamental matter hypermultiplets. To this end, we take profit of a set of first- and second-order equations for the logarithmic derivatives of the prepotential with respect to the dynamical scale expressed in terms of Riemann's theta-function. These equations emerge in the context of the Whitham hierarchy approach to the low-energy Seiberg--Witten solution of supersymmetric gauge theories. Our procedure is recursive and allows to compute the effective prepotential to arbitrary order in a remarkably straightforward way. General expressions for up to three-instanton corrections are given. We illustrate the method with explicit expressions for several cases.