Solution
= Solution
The standard <Fourier series> is
$$
f(x)\sim\frac{a_0}{2}+\sum_{n=1}^\infty(a_n\cos nx+b_n\sin nx),
$$
with <Fourier coefficients>
$$
\boxed{a_n=\frac1\pi\int_{-\pi}^\pi f(x)\cos nx\,dx\quad(n\geq0),\qquad
b_n=\frac1\pi\int_{-\pi}^\pi f(x)\sin nx\,dx\quad(n\geq1)}.
$$
These follow by taking <inner products> with the individual <basis vectors> and using their <orthogonality> and squared <norms>.