Fourier cosine series

A series representation of a function on [0, L] using a constant term plus cosines of integer multiples of pi*x/L.

The Fourier cosine series of $f$ on $[0,L]$ is $f(x)\sim\dfrac{a_0}2+\sum_{n=1}^\infty a_n\cos\dfrac{n\pi x}{L}$ , with $a_n=\dfrac2L\displaystyle\int_0^Lf(x)\cos\dfrac{n\pi x}{L}\,dx$ obtained by projecting $f$ onto each cosine using the orthogonality of the cosine functions on $[0,L]$ .