what is mean deforming $\Gamma$ into the real axis. $\Gamma$ is the contour $\{Im(z)= - \frac{a}{2b^{\frac{1}{2}}}\}$, $z=b^{\frac{1}{2}}x-\frac{a }{2b^{\frac{1}{2}}}i\} $, $a,b\in R$, $b>0$.I am reading Partial Differential Equations, Evans. Page 187.
The statement say $\int_{\Gamma} e^{-z^2}dz = \int_{-\infty}^{\infty}e^{-x^2}dx $ . Can somebody tell me what is mean deforming the contour please, is translate or change of the region ? thank you