Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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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# Complex integral in finite contour at semiaxis

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