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An analytic solution for a fourier transform

  1. Mar 9, 2014 #1
    1. The problem statement, all variables and given/known data
    the function is Exp[-w^2]/w^2, how to solve the Fourier transform analytically with Residue theorem?
    It is better if there is more general results.
    Mathematica can solve it analytically, but I need a human-soluable way.


    2. Relevant equations



    3. The attempt at a solution
    My attempt follows the Fresnel integral, but there is still something wrong.
     
  2. jcsd
  3. Mar 10, 2014 #2

    vanhees71

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    Science Advisor
    2016 Award

    The integral is undefined as it stands, because there's the pole at [itex]\omega=0[/itex]. You have to specify how to run around this pole first!
     
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