Results 1 to 4 of 4

Math Help - Fourier Series Question

  1. #1
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1

    Fourier Series Question

    Think this is a pretty simple question, just getting stuck on the last section, here's what I've got:

    Let f be a periodic function with period 6, such that f(x) = x \: \text{for} \: -3 < x \leq 3. Calculate the Fourier series of f.

    Odd function, so we know a_0 = a_n = 0.

    b_n = \frac{2}{3} \int_0^3 x \cos{\frac{\pi n}{3} x} \: dx

    ...

    = \frac{6}{\pi^2n^2}(\cos{\pi n} - \cos{0})

    = \frac{6}{\pi^2n^2}((-1)^n - 1).

    However in the answer they've got:

    \frac{6}{\pi} \displaystyle\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}\sin{\frac{\pi n}{3} x}.

    Just wondering how they get to the \frac{6}{\pi} \frac{(-1)^{n+1}}{n}, as far as I can see my integration's correct?

    Thanks in advance for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by craig View Post
    Think this is a pretty simple question, just getting stuck on the last section, here's what I've got:

    Let f be a periodic function with period 6, such that f(x) = x \: \text{for} \: -3 < x \leq 3. Calculate the Fourier series of f.

    Odd function, so we know a_0 = a_n = 0.

    b_n = \frac{2}{3} \int_0^3 x \cos{\frac{\pi n}{3} x} \: dx

    ...

    = \frac{6}{\pi^2n^2}(\cos{\pi n} - \cos{0})

    = \frac{6}{\pi^2n^2}((-1)^n - 1).

    However in the answer they've got:

    \frac{6}{\pi} \displaystyle\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}\sin{\frac{\pi n}{3} x}.

    Just wondering how they get to the \frac{6}{\pi} \frac{(-1)^{n+1}}{n}, as far as I can see my integration's correct?

    Thanks in advance for the help

    As far as I can see your answer's correct, and I wonder what happened to the squared pi and n in the denominator, not to mention

    the numerator.

    Is this from some book? Perhaps you misread the number of the question...?

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    I don't think so. I'll try find the questions and post them here.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Here's the question:

    Fourier Series Question-question.jpg

    And here's the answer. Sorry about the quality, this is how I received it. There's no indication as to how they've come by the answer as far as I can tell.

    It's solution number 2 by the way.

    Fourier Series Question-7sol.pdf

    Thanks for the relpy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fourier series question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 5th 2011, 02:01 AM
  2. question about sum of fourier series
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: April 5th 2011, 07:56 AM
  3. Question about Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 21st 2011, 04:33 AM
  4. Fourier Series Question
    Posted in the Calculus Forum
    Replies: 13
    Last Post: March 13th 2011, 09:12 AM
  5. A question on Fourier series
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 1st 2008, 11:54 PM

Search Tags


/mathhelpforum @mathhelpforum