Factorial of Half/Proof 2

Proof
From Infinite Product of Product of Sequence of n plus alpha over Sequence of n plus beta:

Setting:
 * $k = 2$
 * $\alpha_1 = \alpha_2 = 0$
 * $\beta_1 = -\dfrac 1 2, \beta_2 = \dfrac 1 2$

we see that:
 * $\alpha_1 + \alpha_2 = \beta_1 + \beta_2$

So this reduces to:

We then note that by Wallis's Product:
 * $\displaystyle \prod_{n \mathop \ge 1} \dfrac n {n - \frac 1 2} \dfrac n {n + \frac 1 2} = \frac \pi 2$

Thus: