Before revision:  We use two different methods to calculate the expectations E[X_{1}^{2}f(X)] for any measurable function f satisfying some regular conditions. Applying this result, we obtain recursion formulae for product moments of multivariate Gaussian random variablesand multivariate elliptical random variables ^{2}f(X)}]  .
After revision:  We use two different methods to calculate the expectations E[X_{1}^{2}f(X)] for any measurable function f satisfying some regularity conditions. Then, by applying this result, we obtain recursion formulae for product moments of multivariate Gaussian random variablesand multivariate elliptical random variables ^{2}f(X)}] .