Extensión PERIÓDICA (serie de Fourier con periodo p=L)

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

$$a_{0}={\frac {2}{L}}\int _{-L}^{L}f(x)dx$$

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

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