9. Remark 2.12.3 - formula for sin(z)

We may apply the previous theorem to determine that $\prod_{n = 1}^{\infty} (1 - \frac{z^{2}}{n^{2}})$ converges 1;;locally uniformly to a holomorphic funtion. From some algebraic manipulation, we get the identity:

\sin (π z) = π z \prod_{n = 1}^{\infty} (1 - \frac{z^{2}}{n^{2}})