Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex integral with singularity

  1. Mar 14, 2008 #1
    Hi all!

    I am not so deep into complex analysis. So, for the following integral

    [tex]
    \[
    e^{ - \frac{1}
    {4}\int {\partial _{\bar x} \ln \left( {\left| \omega \right|^2 + 1} \right)d\bar x} }
    \]
    [/tex]

    (where [tex]\bar x = x_0 - i x_1[/tex])I did some naive

    [tex]
    \[
    e^{ - \frac{1}
    {4}\int {\partial _{\bar x} \ln \left( {\left| \omega \right|^2 + 1} \right)d\bar x} } = e^{ - \frac{1}
    {4}\left. {\ln \left( {\left| \omega \right|^2 + 1} \right)} \right|_0^{\bar x} }
    \]
    [/tex]

    Because the (analytic) function [tex]\omega[/tex] gets infinity for x = 0, the result doesn't make sense. I guess I failed in handling the singularities. Moreover I don't know on which line to integrate in the complex plane - from the problem itself there is no outstanding one.

    Hope somebody can give me some hints!

    A big thanks in advance, its really important!!

    Blue2script
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted