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Fourier series

Fourier coefficient

{c}

When regularity and convergence justify termwise differentiation, the derivative of a Fourier mode multiplies its coefficient by its frequency. For period $L$,
$$
\widehat{f'}_n=\frac{2\pi in}{L}\widehat f_n.
$$


Termwise differentiation of a Fourier series

Fourier series of a periodically extended quadratic arch

Fourier series of a periodic sawtooth

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Termwise differentiation of a Fourier series

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Termwise differentiation of a Fourier series

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