Solution
= Solution
For a real $2L$-periodic square-integrable function with the convention $f\sim a_0/2+\sum_{n\geq1}(a_n\cos(n\pi x/L)+b_n\sin(n\pi x/L))$, <Parseval's identity> is
$$
\boxed{\frac1L\int_{-L}^L|f(x)|^2dx
=\frac{a_0^2}{2}+\sum_{n=1}^{\infty}(a_n^2+b_n^2).}
$$
It states that the squared <L2 norm> equals the sum of the squared components in the orthogonal <Fourier basis>, with the normalization factors shown. In the present even-function case every $b_n$ vanishes.