Fourier series and the dirchlet integral

[dirk_mec1]

Use a Fourier series to prove that: $$\int_{0}^{ \infty} \frac{\sin(x)}{x}\ \mbox{d}x = \frac{ \pi}{2}$$


What function do I need to Fourier transform?

 

[Pere Callahan]

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.

 

[dirk_mec1]

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.

 

[Pere Callahan]

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 ..?