Some notations and preliminaries first. Let us suppose we denote a standard gaussian density as [$]p(X) \, = \, \frac{1}{2 \pi} \exp(- \, \frac{ X^2 }{2})[$] We also have hermite polynomials and first few hermite polynomials are denoted as [$]H_0(X) \, = \, 1[$] [$]H_1(X) \, = \, X[$] [$]H_2(X) \...