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Fourier series periodic function

  1. Jan 23, 2008 #1
    1. The problem statement, all variables and given/known data
    The following specification of coefficients defines a Fourier series:
    [tex]a_{0}=\frac{2}{\pi};&a_{1}=\frac{1}{2};&a_{n}=\left\{\begin{array}{cc}-\frac{2}{\pi}(-1)^\frac{n}{2}\frac{1}{n^2-1}&\mbox{ for }n\mbox{ even }\\0&\mbox{ for }n\mbox{ odd}\end{array}\right.(\mbox{for }n\geq2);
    \\ \mbox{and}
    \\b_n=0\mbox{ for all }n[/tex]

    2. Relevant equations
    [tex]f(x)=a_0+\sum a_n\cos(nx)+\sum b_n\sin(nx)[/tex]

    3. The attempt at a solution
    I graphed this up to n=4 and it resembles semi-circles on top of a line, and I'm supposed to figure out what "particular periodic function this is. Anyone know?
  2. jcsd
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