Results 1 to 2 of 2

Math Help - Fourier Series

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    39

    Fourier Series

    solved thanks
    Last edited by gomes; October 9th 2010 at 01:37 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by gomes View Post



    To calculate the fourier series, I used the formulae above, and I got:



    and i substituted the values into the equation:


    1. So what would my next step be? How do i show that the fourier series is given by the equation in the questions?

    2. and using those results, how do i calculate 1-(1/4)+(1/9)-(1/16)+... and the 1/(n^2) sum to infinity?

    Thanks

    You may want to open up the sum you got: it's exactly the same as in the question, so you already have (1)

    As for (2): according to what you wrote: 0=f(0)=\frac{\pi^2}{3}+4\sum\limits^\infty_{n=1}\f  rac{(-1)^n}{n^2}\Longrightarrow \sum\limits^\infty_{n=1}\frac{(-1)^{n-1}}{n^2}=\frac{\pi^2}{12}.

    Likewise: \pi^2=f(\pi)=\frac{\pi^2}{3}+4\sum\limits^\infty_{  n=1}\frac{1}{n^2}\Longrightarrow ....get the sum

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Fourier series to calculate an infinite series
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 4th 2010, 02:49 PM
  2. Complex Fourier Series & Full Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2009, 06:39 AM
  3. fourier series again
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: January 25th 2009, 04:46 PM
  4. Fourier series
    Posted in the Calculus Forum
    Replies: 10
    Last Post: February 2nd 2008, 04:42 AM
  5. from fourier transform to fourier series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2008, 07:35 AM

Search Tags


/mathhelpforum @mathhelpforum