Prepotentials in N=2 SU(2) Supersymmetric Yang-Mills Theory with Massless Hypermultiplets

We calculate the prepotential of the low-energy effective action for $N=2$ $SU(2)$ supersymmetric Yang-Mills theory with $N_f$ massless hypermultiplets ($N_f=1,\, 2,\, 3$). The precise evaluation of the instanton corrections is performed by making use of the Picard-Fuchs equations associated with elliptic curves. The flavor dependence of the instanton effect is determined explicitly both in the weak- and strong-coupling regimes.