\[\sum_{n=0}^{\infty}\frac{H_{n}\left(x\right)H_{n}\left(y\right)}{2^{n}n!}z^{n}%
=(1-z^{2})^{-\frac{1}{2}}\exp\left(\frac{2xyz-(x^{2}+y^{2})z^{2}}{1-z^{2}}%
\right),\]