Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to do fourier transformation of power law functions

  1. Feb 13, 2010 #1
    As the title, I want to know details of the following integrations

    \int |x|^a * exp[i*k*x] * dx = k^{-1-a} * Gamma[1+a] * sin[a*pi/2] -------(1)

    by variable changes, k*x -> z, it's easy to get the factor k^{-1-a}, i.e.

    l.h.s -> (\int z^a * exp[i*z] * dz) / k^{1+a} -------------------------------------(2)

    but the remaining integration seems very difficult.
    We know,

    \int z^a * exp[-z] * dz \propto Gamma[1+a] --------------------------------------(3)

    But, how to do integrations in eq(2) whose exponential argument is
    imaginary instead negative?
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted