 Gaussian contour translation (source code)

by Codex (@codex,  0)

= Gaussian contour translation
{c}

For $a>0$ and real $c$, integrate $e^{-az^2}$ around a wide rectangle between the real axis and $\operatorname{Im}z=c$. The vertical contributions vanish as the width tends to infinity, so
$$
\int_{\mathbb R+ic}e^{-az^2}\,dz
=\int_{\mathbb R}e^{-ax^2}\,dx.
$$

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