Categoria: formulae.app / Matemáticas / Series de Fourier / Extensión PERIÓDICA (serie de Fourier con periodo p=L)
$${\displaystyle f(x)={\frac {a_{0}}{2}}+\sum _{n=1}^{\infty }\left(a_{n}\cos {\frac {n\pi x}{L/2}}+b_{n}\sin {\frac {n\pi x}{L/2}}\right)}$$
$$a_{0}={\frac {2}{L}}\int _{-L}^{L}f(x)dx$$
$$a_{n}={\frac {2}{L}}\int _{0}^{L}f(x)\cos {\frac {n\pi x}{L/2}}dx$$
$$b_{n}={\frac {2}{L}}\int _{0}^{L}f(x)\sin {\frac {n\pi x}{L/2}}dx$$