Difference between revisions of "Weierstrass factorization of sine"
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$$\sin(z) = z \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{z^2}{k^2\pi^2} \right),$$ | $$\sin(z) = z \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{z^2}{k^2\pi^2} \right),$$ | ||
where $\sin$ is the [[sine]] function. | where $\sin$ is the [[sine]] function. | ||
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==Proof== | ==Proof== | ||
==References== | ==References== | ||
Revision as of 00:31, 4 June 2016
Theorem
The following formula holds: $$\sin(z) = z \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{z^2}{k^2\pi^2} \right),$$ where $\sin$ is the sine function.
