Difference between revisions of "Sinc"
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<strong>Theorem:</strong> The following formula holds: | <strong>Theorem:</strong> The following formula holds: | ||
| − | $$\mathrm{ | + | $$\mathrm{sinc}(x)=\displaystyle\prod_{k=1}^{\infty} \cos \left( \dfrac{x}{2^k} \right).$$ |
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
Revision as of 02:09, 30 April 2015
The $\mathrm{sinc}$ function is defined by $$\mathrm{sinc}(x) = \left\{ \begin{array}{ll} \dfrac{\sin x}{x} &; x \neq 0 \\ 1 &; x=0. \end{array} \right.$$
Plot of $\mathrm{sinc}$ on $[-15,15]$.
Properties
Theorem: The following formula holds: $$\mathrm{sinc}(x)=\displaystyle\prod_{k=1}^{\infty} \cos \left( \dfrac{x}{2^k} \right).$$
Proof: █
