A book on which I am studying (Arfken: Mathematical Methods for Physicists), uses the following result in order to derive an asymptotic expansion:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_{0}^{-i\infty} \frac{e^{-xu}}{1+iu}du = \int_{0}^{\infty} \frac{e^{-xu}}{1+iu}du,[/tex]

where the change of limits in the integral is justified by invoking Cauchy's theorem. I am familiar with Cauchy's theorem, but I am not sure why it justifies this passage. How does it work?

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# Cauchy's Theorem

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