Difference between revisions of "Sinc"
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File:Sinc.png|Plot of $\mathrm{sinc}$ on $[-15,15]$. | File:Sinc.png|Plot of $\mathrm{sinc}$ on $[-15,15]$. | ||
| + | File:Complex sinc.png|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{sinc}$ on $[-15,15] \times [-15,15] \subset \mathbb{C}$. | ||
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Revision as of 22:14, 2 May 2015
The $\mathrm{sinc}$ function is defined by $$\mathrm{sinc}(x) = \left\{ \begin{array}{ll} \dfrac{\sin x}{x} &; x \neq 0 \\ 1 &; x=0. \end{array} \right.$$
Plot of $\mathrm{sinc}$ on $[-15,15]$.
- Complex sinc.png
Domain coloring of analytic continuation of $\mathrm{sinc}$ on $[-15,15] \times [-15,15] \subset \mathbb{C}$.
Properties
Theorem: The following formula holds: $$\mathrm{sinc}(x)=\displaystyle\prod_{k=1}^{\infty} \cos \left( \dfrac{x}{2^k} \right).$$
Proof: █
