\[H_{m}\left(x\right)H_{n}\left(x\right)=\sum_{\ell=0}^{\min(m,n)}\genfrac{(}{)}%
{0.0pt}{}{m}{\ell}\genfrac{(}{)}{0.0pt}{}{n}{\ell}2^{\ell}\ell!H_{m+n-2\ell}%
\left(x\right).\]