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!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted