Meromorphic scaling flow of N=2 supersymmetric SU(2) Yang-Mills with matter

beta-functions are derived for the flow of N = 2 SUSY SU(2) Yang-Mills in 4-dimensions with massless matter multiplets in the fundamental representation of the gauge group. The beta-functions represent the flow of the couplings as the VEV of the Higgs field is lowered and are modular forms of weight -2. They have the correct asymptotic behaviour at both the strong and weak coupling fixed points. Corrections to the massless beta-functions when masses are turned on are discussed. (c) 2006 Elsevier B.V. All rights reserved.