Results 1 to 2 of 2

Math Help - Integration to find the Fourier coefficients

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    3

    Question Integration to find the Fourier coefficients

    Hi, I want to calculate the Fourier series expansion of

    f(x)= a sin(x) / (1-2 a cos(x) + a^2), where |a|<1 and -pi < x <pi,

    but I cannot integrate the function "cos(nx) f(x)". Is there a trick for this integration. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Gaudium View Post
    Hi, I want to calculate the Fourier series expansion of

    f(x)= a sin(x) / (1-2 a cos(x) + a^2), where |a|<1 and -pi < x <pi,

    but I cannot integrate the function "cos(nx) f(x)". Is there a trick for this integration. Thanks.
    Observe that:

    f(x)=\frac{d}{dx} \left[ \frac{1}{2}\ln(1-2a \cos(x)+a^2)\right]

    then integration by parts will help

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fourier Coefficients
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 10th 2011, 07:34 AM
  2. Fourier Coefficients?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 29th 2010, 08:43 AM
  3. Fourier Coefficients
    Posted in the Differential Geometry Forum
    Replies: 11
    Last Post: June 23rd 2009, 07:50 PM
  4. Fourier Coefficients
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 1st 2009, 07:28 AM
  5. find Fourier coefficients
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 24th 2007, 10:33 AM

Search Tags


/mathhelpforum @mathhelpforum