Results 1 to 2 of 2

Math Help - fourier coefficients

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    114

    fourier coefficients

    Find the Fourier cosine coefficients of  e^x


     e^x = \frac{1}{2}a_0 + \displaystyle\sum_{n=1}^\infty a_n cos \frac{n \pi x}{L}

    Differentiating yields:

     e^x = - \displaystyle\sum_{n=1}^\infty \frac{n \pi}{L}a_n sin \frac{n \pi x}{L},

    the Fourier sine series of e^x. Differentiating again yields

     e^x = - \displaystyle\sum_{n=1}^\infty (\frac{n \pi}{L})^2 a_n cos \frac{n \pi x}{L},

    Since equations 1 and 3 both give Fourier cosine series of e^x, they must be identical. Thus,

     a_o = 0 and  a_n = 0.


    Can anyone please explain step by step what is wrong with this? I'm supposed to correct the mistakes and then find a_n without using the typical technique but I'm so confused!

    Any mistakes at all you can see, please point them out!

    Thanks in advance
    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 hunkydory19 View Post
    Find the Fourier cosine coefficients of  e^x


     e^x = \frac{1}{2}a_0 + \displaystyle\sum_{n=1}^\infty a_n cos \frac{n \pi x}{L}

    Differentiating yields:

     e^x = - \displaystyle\sum_{n=1}^\infty \frac{n \pi}{L}a_n sin \frac{n \pi x}{L},

    the Fourier sine series of e^x. Differentiating again yields

     e^x = - \displaystyle\sum_{n=1}^\infty (\frac{n \pi}{L})^2 a_n cos \frac{n \pi x}{L},

    Since equations 1 and 3 both give Fourier cosine series of e^x, they must be identical. Thus,

     a_o = 0 and  a_n = 0.


    Can anyone please explain step by step what is wrong with this? I'm supposed to correct the mistakes and then find a_n without using the typical technique but I'm so confused!

    Any mistakes at all you can see, please point them out!

    Thanks in advance
    What are the conditions under which you can differentiate a series term by term?

    Have you considered integrating twice (and then expressing the integral as
    a cosine series)?

    RonL
    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, 06:34 AM
  2. Fourier Coefficients?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: May 29th 2010, 07:43 AM
  3. Fourier coefficients
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 7th 2010, 11:36 PM
  4. Fourier Coefficients
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 1st 2009, 06:28 AM
  5. Fourier coefficients
    Posted in the Advanced Math Topics Forum
    Replies: 10
    Last Post: December 31st 2008, 03:05 PM

Search Tags


/mathhelpforum @mathhelpforum