# Fourier series periodic function

1. Jan 23, 2008

### dpackard

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

2. Relevant equations
$$f(x)=a_0+\sum a_n\cos(nx)+\sum b_n\sin(nx)$$

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?