Difference between revisions of "Weierstrass factorization of sine"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | 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),$$ |
| + | where $\sin$ is the [[sine]] function. | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
| + | |||
| + | ==Proof== | ||
| + | |||
| + | ==References== | ||
Revision as of 00:31, 4 June 2016
Theorem
The following formula holds: $$\sin(z) = z \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{z^2}{k^2\pi^2} \right),$$ where $\sin$ is the sine function.
Proof: █
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