Series - Fourier series

Integrable function : f(x)

Fourier coeffieients : \(a_0,a_n, b_n\)

Whole number : n

  1. \(f(x)= {a_0 \over 2}+ \displaystyle\sum_{n=1}^\infty (a_n \; cos \, nx+ b_n \; sin \; nx)\)
  2. \(a_n= {1 \over \pi} \int\limits_{-\pi}^\pi f(x)cos \, nx \, dx\)
  3. \(b_n= {1 \over \pi} \int\limits_{-\pi}^\pi f(x)sin \, nx \, dx\)