Applied Mathematics/Fourier Cosine Series

Fourier cosine series
The series below is called Fourier cosine series.
 * $$f(x)=\frac{a_0}{2}+\sum_{n=1}^\infty a_n \cos \frac{n \pi x}{L}$$

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