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

Fourier series and the dirchlet integral

  1. Jun 5, 2008 #1
    Use a Fourier series to prove that: [tex] \int_{0}^{ \infty} \frac{\sin(x)}{x}\ \mbox{d}x = \frac{ \pi}{2} [/tex]


    What function do I need to fourier transform?
     
  2. jcsd
  3. Jun 7, 2008 #2
    There aren't many to choose from are they? I suggest you try Fourier-transforming sin(x) and sin(x)/x and see where it leads you.
     
  4. Jun 7, 2008 #3
    Actually there are and I found that there are two ways of finding this answer both NOT with solely a sin(x) or sin(x)/x. I'm suprised that you didn't took the effort to look more closely to the question at hand.
     
  5. Jun 7, 2008 #4
    You're right. In particular I read Fouriertransform instead of Fourier Series. You're also right in saying that transforming sin(x) or sin(x)/x seems not to provide an easy solution to the problem.

    Which two ways are you referring to? One is likely to Laplace-transform 1/x ..?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fourier series and the dirchlet integral
  1. Fourier Series (Replies: 1)

  2. Fourier Series (Replies: 1)

  3. Fourier series (Replies: 1)

  4. Fourier Series (Replies: 1)

Loading...