Fourier series periodic function

  • Thread starter dpackard
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Homework Statement


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]



Homework Equations


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



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?
 

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