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The normalized sinc function is $\sin (\pi x)/(\pi x)$ away from zero and one at zero. The value at zero removes the apparent singularity, giving an entire function. Its nonzero integer zeros make it useful for Sampling Theory.

With the cycles-per-unit Fourier transform convention, the inverse transform of the unit-width rectangle isThe factor of $\pi$ is therefore tied to a frequency convention. The unnormalized sinc function uses $\sin x/x$ instead, so the two names must be distinguished when comparing formulas.