Results 1 to 4 of 4

Math Help - fourier series again

  1. #1
    Member
    Joined
    Jan 2009
    Posts
    83

    fourier series again

    f(x) = xsin(px)

    to calculate the fourier series, I am struggling.. do I need to distinguish between when p = n?

    I am really struggling with the integration of this.. could somebody please show me how I would go about it? many thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,367
    Thanks
    42
    Quote Originally Posted by James0502 View Post
    f(x) = xsin(px)

    to calculate the fourier series, I am struggling.. do I need to distinguish between when p = n?

    I am really struggling with the integration of this.. could somebody please show me how I would go about it? many thanks
    Is p a positive integer?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    Posts
    83
    yes, sorry, that wasnt clear

    any help would be so greatly appreciated!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,367
    Thanks
    42
    Quote Originally Posted by James0502 View Post
    yes, sorry, that wasnt clear

    any help would be so greatly appreciated!
    Here's what I got

    a_0 = \frac{1}{\pi} \int_{- \pi}^{\pi} x \sin p x\, dx = - \frac{2 (-1)^p}{p}

    a_n = \frac{1}{\pi} \int_{- \pi}^{\pi} x \sin p x \cos nx\, dx = - \frac{2 p}{p^2 -n^2}\,(-1)^{p+n}\;\;\;n \ne p

    a_n = - \frac{1}{2p},\;\;\;n = p

    The series

    \frac{a_0}{2} + \sum_{i=1}^{\infty} a_n \cos nx
    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, 01:49 PM
  2. Complex Fourier Series & Full Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2009, 05:39 AM
  3. Fourier Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 15th 2009, 09:30 AM
  4. Fourier series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 9th 2008, 09:51 PM
  5. from fourier transform to fourier series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2008, 06:35 AM

Search Tags


/mathhelpforum @mathhelpforum