1. Not finding help here? Sign up for a free 30min 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!

Fourier Series

  1. Mar 19, 2008 #1
    Use the Fourier series technique to show that the following series sum to the quantities shown:
    1+1/3^2+1/5^2+...+1/n^2=pi^2/8 for n going to infinity

    I foudn the series to be:


    but I don't know how to prove the idenity.

    I don't know how to go about solving it using the Fourier method. Any help would be greatly appreciated, thanks!

    I was able to prove sum(1/n^4,n,1,infinity)=pi^4/90 and sum(1/n^2,n,1,infinity)=pi^2/6 and I'm not sure if the problem is simular.
  2. jcsd
  3. Mar 23, 2008 #2
    Calculate the Fourier series of the following function:
    [tex]f(x)=|x| \qquad -\pi<x<\pi[/tex]
    [tex]f(x)=-x \qquad -\pi<x<0[/tex]
    [tex]f(x)=x \qquad 0<x<\pi[/tex]
    with period [itex]2\pi[/itex]. After this set x=0 in the resulting series and you arrive at the result.
  4. Mar 27, 2008 #3

    Thanks I got it
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Fourier Series
  1. The Fourier series (Replies: 1)