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Using an Environmentally Friendly Renormalization Group we derive an abinitio universal scaling form for the equation of state for the O(N) model,y=f(x), that exhibits all required analyticity properties in the limits $x\to0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on aphenomenological scaling ansatz the scaling function is derived solely from theunderlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the threeWilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$ whichexhibit a non-trivial crossover between the Wilson-Fisher fixed point and thestrong coupling fixed point associated with the Goldstone modes on thecoexistence curve. We give explicit results for N=2, 3 and 4 to one-loop orderand compare with known results.

An ab initio Calculation of the Universal Equation of State for the O(N) Model