Fourier Transform--Heaviside Step Function

$${\mathcal F}[H(x)] = \int_{-\infty}^\infty e^{-2\pi ikx}H(x)\,dx = {1\over 2}\left[{\delta(k)-{i\over \pi k}}\right],$$

where $H(x)$ is the Heaviside Step Function and $\delta(k)$ is the Delta Function.

See also Heaviside Step Function