1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Contour Integral: confusion about cosine/sine

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data
    I am to integrate cos(2x)/(x-i*pi) from -inf to inf


    2. Relevant equations



    3. The attempt at a solution
    The problem I'm having is this:

    I write cos(2x) in exponential form, e^(2iz), so f(z) = e^(2iz)/(z-i*pi). I choose a large semicircle in the UHP as my contour. At large R, the integral over the arc goes to 0.

    There is a simple pole at z=i*pi. The residue at the simple pole is then lim z-->i*pi [e^(2iz)] = e^(-2pi), so I get the integral to be 2*pi*i*e^(-2pi). But the answer is pi*i*e^(-2pi), half of what I get.

    This answer can be gotten if one writes cos(2z) in the UHP as 1/2(e^(2iz)), but other problems with sine or cosine I have successfully solved writing sine or cosine without using this factor of 1/2. What am I missing here?
     
  2. jcsd
  3. Oct 9, 2011 #2
    Nevermind. I see. The associated term with sine is not odd in this case, so we cannot just use e^(2iz).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Contour Integral: confusion about cosine/sine
Loading...