Fourier cosine series

The series below is called Fourier cosine series.

${\displaystyle f(x)={\frac {a_{0}}{2}}+\sum _{n=1}^{\infty }a_{n}\cos {\frac {n\pi x}{L}}}$

where

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