Factorial of Half/Proof 1
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Theorem
- $\left({\dfrac 1 2}\right)! = \dfrac {\sqrt \pi} 2$
Proof
| \(\ds \paren {\dfrac 1 2}!\) | \(=\) | \(\ds \map \Gamma {1 + \dfrac 1 2}\) | Gamma Function Extends Factorial | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 2 \map \Gamma {\dfrac 1 2}\) | Gamma Difference Equation | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 2 \sqrt {\pi}\) | Gamma Function of One Half |
$\blacksquare$