Fourier sine series

The series below is called Fourier sine series.

${\displaystyle f(x)=\sum _{n=1}^{\infty }b_{n}\sin {\frac {n\pi x}{L}}}$

where

${\displaystyle b_{n}={\frac {2}{L}}\int _{0}^{L}f(x)\sin {\frac {n\pi x}{L}}dx}$