What is the value of $\left(\frac 12\right)!$ ?

**
Notation:
**
$!$
denotes the
factorial notation
. For example
$8!=1\times 2\times 3 \times 4 \times 5 \times 6 \times 7 \times 8$
.

not possible
0.886227..
infinite
0.234971..

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

The gamma function serves as an extension of the factorial function beyond the non-negative integer. And one of the functional equations is $\Gamma (s) = (s-1)!$ . Therefore,

$\begin{aligned} \left(\frac 12\right) ! & = \Gamma \left(\frac 32\right) & \small \color{#3D99F6} \text{Using the identity: }\Gamma (s+1) = s\Gamma (s) \\ & = \frac 12 \Gamma \left(\frac 12\right) & \small \color{#3D99F6} \text{Note that }\Gamma \left(\frac 12\right) = \sqrt \pi \\ & = \frac {\sqrt \pi}2 \\ & = \boxed{0.8862269...} \end{aligned}$