\[\frac{1}{2\pi}\int_{-\infty}^{\infty}{\mathrm{e}}^{-t^{2}/(4n)}{\mathrm{e}}^{%
\mathrm{i}(x-a)t}\,\mathrm{d}t=\sqrt{\frac{n}{\pi}}{\mathrm{e}}^{-n(x-a)^{2}}.\]