Gamma Function of 3 over 2
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Theorem
- $\map \Gamma {\dfrac 3 2} = \dfrac {\sqrt \pi} 2$
where $\Gamma$ denotes the Gamma function.
Proof
| \(\ds \map \Gamma {\dfrac 3 2}\) | \(=\) | \(\ds \map \Gamma {\dfrac 1 2 + 1}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 2 \map \Gamma {\dfrac 1 2}\) | Gamma Difference Equation | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {\sqrt \pi} 2\) | Gamma Function of One Half |
$\blacksquare$