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Tricky integral

  1. Jun 8, 2014 #1
    1. The problem statement, all variables and given/known data
    [itex]\int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dk[/itex]

    2. Relevant equations

    3. The attempt at a solution
    As you can guess, this is the inverse Fourier transform of [itex]|k|^{2\lambda}[/itex]. I've tried splitting it from -infinity to 0 and 0 to infinity. I've tried noting that |k| is even, cos is even, sin is odd and getting:

    [itex]2\int_0^{\infty} |k|^{2\lambda}\cos(kx)dk [/itex]
    But this integral doesn't even converge.
  2. jcsd
  3. Jun 9, 2014 #2


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    Science Advisor
    Gold Member

    I don't think the original integral converges either, no matter what the value of ##\lambda## is. Try using different values of ##\lambda## and ##x## and integrating numerically with a large interval of integration.
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