Effective Potential for a Renormalizedd-Dimensionalgϕ4Field Theory in the Limitg→∞

The first four coefficients in the effective potential $V_{\mathrm{eff}}\left({\varphi }_R\right)=\Sigma {n=1\mathrm{}}^{\infty } V_{2n}{{\varphi }_R}^{2n}$ are calculated for a mass- and wave-function-renormalized $g{\varphi }^4$ field theory in $d$ space-time dimensions in the limit where the unrenormalized coupling $g\to \infty$ with the renormalized mass $M$ held fixed. The accuracy of these numerical results is verified by exact analytical calculations of the effective potential performed in 0 and 1 space-time dimensions.