$S(f)(x)=\frac{a_0}{2}+\sum{a_n\cos{(n\omega x)}}+\sum{b_n\sin{(n\omega x)}}$ 
où $\cases{a_n=2<f, \cos{(n\omega x)}>=\boxed{\frac{2}{T}\int_{x_0}^{x_0+T}f(x)\cos{(n\omega x)}dx} \\ b_n=2<f, \sin{(n\omega x)}>=\boxed{\frac{2}{T}\int_{x_0}^{x_0+T}f(x)\sin{(n\omega x)}dx}}$  

$\frac{a_0}{2} \rightarrow$Valeur moyenne de $f$: $\frac{1}{T}\int_{x_0}^{x_0+T}f(x)dx$

![[c307a9893a.pdf]]

![[IMG_7785.jpeg]]