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F. transform problem

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data

    Find Fourier transform of function

    [tex]f(x)=\frac{1}{x^2+a^2}[/tex], [tex]a>0[/tex]

    2. Relevant equations


    3. The attempt at a solution

    Two different case




    How to solve integral


    Probably using complex analysis?! I forget this. I have two poles [tex]ia[/tex] and [tex]-ia[/tex]. How to integrate this? Is there some other method without using complex analysis?
  2. jcsd
  3. Oct 29, 2011 #2
    "Is there some other method without using complex analysis?"

    Nope. But complex analysis isn't that bad -- it just seems like black magic until you get used to it. You might want to look at the example at http://en.wikipedia.org/wiki/Residue_theorem .
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