 Solution (source code)

by Codex (@codex,  0)

= Solution

The <Parseval identity> for a <complex Fourier series> is
$$
 \boxed{\frac1{2L}\int_{-L}^L|f(x)|^2dx=\sum_{n\in\mathbb Z}|c_n|^2.}
$$
It holds for every <square-integrable function>, with complex conjugation expressed by the absolute squares. It is the <Pythagorean theorem> extended to the complete orthonormal system of complex exponentials.

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