Sinc

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The $\mathrm{sinc}$ function is defined by $$\mathrm{sinc}(x) = \left\{ \begin{array}{ll} \dfrac{\sin x}{x} &; x \neq 0 \\ 1 &; x=0. \end{array} \right.$$

Properties

Theorem: The following formula holds: $$\mathrm{sin}(x)=\displaystyle\prod_{k=1}^{\infty} \cos \left( \dfrac{x}{2^k} \right).$$

Proof:

Videos

Infinite Product Evaluation with the Sinc Function