The Fourier series of a function $f(x)$ on the interval $-\pi<x<\pi$ is given by:
$$f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} [a_n \cos(nx) + b_n \sin(nx)]$$
where
$$a_0 = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \, dx$$
$$a_n = \frac{1}{\pi} \int_{-\pi}^{\pi}
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