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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

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# Complex integral with singularity

Can you offer guidance or do you also need help?

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