Applied Mathematics/Fourier Sine Series

Fourier sine series
The series below is called Fourier sine series.
 * $$f(x)=\sum_{n=1}^\infty b_n \sin \frac{n \pi x}{L} $$

where
 * $$b_n=\frac{2}{L}\int_{0}^{L}f(x) \sin \frac{n \pi x}{L}dx$$