  We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model
on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We
calculate the full universal crossover scaling forms for the free energy and
the equation of state. We compare the results obtained using ``environmentally
friendly'' renormalization with those found using a direct, non-renormalization
group approach. A set of effective critical exponents are calculated and
scaling laws for these exponents are shown to hold exactly, thereby yielding
non-trivial relations between the various thermodynamic scaling functions.
