2.v.1 Fourier Series

A periodic function $f$ with period $L$ (subject to certain continuity conditions that I will not detail here) can be written as

\[\boxed{f(x) = a + \sum_{n=1}^{\infty} b_n \cos \left ( \frac{2 \pi n x}{L} \right )+ \sum_{n=1}^{\infty} c_n \sin \left ( \frac{2\pi n x}{L}\right ).}\]