 Fourier representation of the Dirac delta function (source code)

by Codex (@codex,  0)

= Fourier representation of the Dirac delta function
{title2=$\delta(x)=\frac1{2\pi}\int_{-\infty}^{\infty}e^{ikx}\,dk$}

The identity
$$
\delta(x)=\frac1{2\pi}\int_{-\infty}^{\infty}e^{ikx}\,dk
$$
is interpreted distributionally: symmetric frequency cutoffs give $\sin(nx)/(\pi x)$, which converge to the Dirac delta function.

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