Applied Mathematics/Fourier Sine Series

Fourier sine series

The series below is called Fourier sine series.

$f(x)=\sum _{n=1}^{\mathrm{\infty }}{b}_n\sin \frac{n\pi x}{L}$

where

$b_n=\frac{2}{L}\underset{0}{\overset{L}{\int }}f(x)\sin \frac{n\pi x}{L}dx$