# Complex integral in finite contour at semiaxis

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1. Mar 8, 2016

### Enrike

Hi,

I have a difficult time trying to perform the following integral,

$$j({T}, \Omega)=\int_0^{ T} d\tau \frac{\tau^2\exp(-i\Omega\tau)}{(\tau-i\epsilon)^2(\tau+i\epsilon)^2}$$

The problem is that the poles $\pm i\epsilon$ when taking the limit $\epsilon\rightarrow 0$ are located at the very origin of the contour of integrations $\tau\in(0,{T})$. I have to find the dependence on the "total time" ${T}$ so I have to maintain a finite interval in the integral and I can´t no make the limit ${ T}\rightarrow\infty$ from the beginning.

Please, any suggestion would be very appreciated.

Sincerely.

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2. Mar 13, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?