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For <integers> $m$ and $n$,
$$
\int_0^1 e^{2\pi imx}\overline{e^{2\pi inx}}\,dx=
\begin{cases}1,&m=n,\\0,&m\ne n.\end{cases}
$$
This orthogonality extracts matching coefficients when two <Fourier series> are integrated over one period.

Orthogonality of complex exponentials

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 137 / 2 / d / Solution

Orthogonality of complex exponentials

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Orthogonality of complex exponentials

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