 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/ib/paper-4/17d/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

\frac{1}{2 L} \int_{- L}^{L} ∣ f (x) ∣^{2} d x = n \in Z \sum ∣ 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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