Weierstrass factorization theorem
From specialfunctionswiki
Contents
Examples of Weierstrass factorizations
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.
Proof
References
Theorem
The Weierstrass factorization of $\cos(x)$ is $$\cos(x) = \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{4x^2}{\pi^2 (2k-1)^2} \right).$$
