\[\int_{0}^{\infty}{\mathrm{e}}^{-\frac{1}{2}x^{2}}\mathit{He}_{n}\left(x\right)%
\mathit{He}_{n+2m+1}\left(x\right)\sin\left(xy\right)\,\mathrm{d}x=(-1)^{m}%
\sqrt{\tfrac{1}{2}\pi}n!\,y^{2m+1}{\mathrm{e}}^{-\frac{1}{2}y^{2}}L^{(2m+1)}_{%
n}\left(y^{2}\right).\]