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A function as a Fourier series

  1. Sep 5, 2009 #1
    I'm working on a P.D.E. homework problem and the one part of it my professor gave us a function and wants us to set it equal to a given series and find the variable. Specifically, find f(sub n) in

    x-x[tex]^{2}[/tex]=[tex]\sum[/tex] (from n=1 to [tex]\infty[/tex]) f(sub n) sin(n[tex]\pi[/tex]x)

    I'm not sure exactly how to do this. I tried writing out the series, then taking the derivative of both sides and setting x=0 (then repeat process) and trying to find a pattern, but I ended up getting an unequal statement. My attempt there was hoping that something would zero out and I could see how the f is changing from f(sub 0) to f(sub 1) to f(sub 2)... I guess my question is where my logic is wrong and how I should begin the problem instead. Thanks in advance!
     
  2. jcsd
  3. Sep 5, 2009 #2
    Exploit the orthogonality of sine functions.
     
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