Difference between revisions of "Weierstrass factorization of sine"
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The following formula holds: | The following formula holds: | ||
$$\sin(z) = z \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{z^2}{k^2\pi^2} \right),$$ | $$\sin(z) = z \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{z^2}{k^2\pi^2} \right),$$ | ||
| − | where $\sin$ | + | where $\sin$ denotes the [[sine]] function and $\pi$ denotes [[pi]]. |
==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 $\sin$ denotes the sine function and $\pi$ denotes pi.
