Difference between revisions of "Weierstrass factorization of sine"
From specialfunctionswiki
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | ==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),$$ |
| − | + | where $\sin$ denotes the [[sine]] function and $\pi$ denotes [[pi]]. | |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| + | ==References== | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:32, 8 June 2016
Theorem
The following formula holds: $$\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.
