  Using an Environmentally Friendly Renormalization Group we derive an ab
initio 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 $x\to
0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on a
phenomenological scaling ansatz the scaling function is derived solely from the
underlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the three
Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$ which
exhibit a non-trivial crossover between the Wilson-Fisher fixed point and the
strong coupling fixed point associated with the Goldstone modes on the
coexistence curve. We give explicit results for N=2, 3 and 4 to one-loop order
and compare with known results.
