Polynomial Gaussian integration by parts on the canonical product space.

theorem GaussianMomentsCounterexamples.expectation_X_mul {n : ℕ} (i : Fin n) (P : MvPolynomial (Fin n) ℂ) : expectation (MvPolynomial.X i * P) = expectation ((MvPolynomial.pderiv i) P)

Stein's identity for each real coordinate and every complex polynomial.