The density of Hermite forms: \[ h(u)=P^ 2_ k(u-\tau)\Phi^ 2(u| \tau,diag(\gamma)) \] where \(P_ k\) is a polynomial of degree K and \(\Phi\) is the density function of the multivariate normal distribution is shown to be capable of approximating any density arbitrarily closely subject to minimal qualifications relating to compactness, denseness, uniform convergence and identification defined over the parameter space.