\[\frac{\mathrm{d}}{\mathrm{d}x}\left({\mathrm{e}}^{-\frac{1}{2}x^{2}}\mathit{He%
}_{n}\left(x\right)\right)=-{\mathrm{e}}^{-\frac{1}{2}x^{2}}\mathit{He}_{n+1}%
\left(x\right).\]