McMohan's Theorem

Consider a Gaussian Bivariate Distribution. Let $f(x_1,x_2)$ be an arbitrary Function. Then

$${\partial^n\langle f\rangle\over\partial\rho^n} = \left\lang... ...ial^{2n}f\over \partial{x_1}^n\partial{x_2}^n}\right\rangle{}.$$

See also Gaussian Bivariate Distribution