Rodrigues: $H_n(\xi) = (-1)^n e^{\xi^2}\frac{d^n}{d\xi^n}e^{-\xi^2}$ - Recursion: $H_{n+1} = 2\xi H_n - 2nH_{n-1}$ - Orthogonality: $\int_{-\infty}^{\infty} H_m H_n e^{-\xi^2}d\xi = \sqrt{\pi}\,2^n n!\,\delta_{mn}$