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 in finite contour at semiaxis

  1. Mar 8, 2016 #1

    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.


    Attached Files:

  2. jcsd
  3. Mar 13, 2016 #2
    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Complex integral finite Date
I Complex integral Jun 8, 2017
I Complex integral of a real integrand May 5, 2017
A Inverse Laplace transform of a piecewise defined function Feb 17, 2017
I Question about Complex limits of definite integrals Jan 30, 2017
I Complex integral problem Dec 7, 2016