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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cauchy's Theorem

Loading...

Similar Threads - Cauchy's Theorem | Date |
---|---|

Cauchy's theorem on limits | Jul 9, 2015 |

Cauchys theorem | Oct 11, 2011 |

Questions about complex analysis (Cauchy's integral formula and residue theorem) | Apr 27, 2011 |

Bolzano-wierstrass theorem and its dilemma when applied to cauchy sequence | Oct 19, 2010 |

Complex Analysis: Cauchy's Theorem | May 4, 2010 |

**Physics Forums - The Fusion of Science and Community**