- #1
Enrike
- 1
- 0
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.
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.