Fourier series and the dirchlet integral

  • Thread starter dirk_mec1
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  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #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.
 
  • #3
761
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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.
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.
 
  • #4
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.
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 ..?
 

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