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Homework Help: Finding the Fourier series of a function.

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    -cos(x) when -π<x<0
    cos(x) when 0<x<π

    Decide if f is an even, odd function or either.
    Find the Fourier series of f.

    2. Relevant equations

    odd function: f(x)=f(-x)
    even function: -f(x)=f(-x) or f(x)=-f(-x)

    3. The attempt at a solution

    substitute -x into either cos(x) or -cos(x) => -cos(x)=-cos(-x) and cos(x)=cos(-x),
    therefore, f is an even function.

    However, I'm stuck when it comes to finding the Fourier series.

    I know how to solve a0, where I just need to find the integration of -cos(x)dx and cos(x)dx. To find an and bn, I need to find the integration of [-cos(x)cos(nx)dx], [cos(x)cos(nx)dx], [-cos(x)sin(nx)] and [cos(x)sin(nx)dx]. I tried to solve them using integration by parts, but it turned out to be infinitely expanding, so I guess integration by parts won't work. Is there any other way to integrate the above four functions?
  2. jcsd
  3. Dec 7, 2011 #2

    Ray Vickson

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    Your definitions of "even" and "odd" are the exact opposite of everybody else's in the world.

  4. Dec 7, 2011 #3


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    You need the product formulas:

  5. Dec 7, 2011 #4
    I just typed it wrong but they wouldn't let me edit it. :(
  6. Dec 7, 2011 #5
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