# Gamma Function of Minus One Half

## Theorem

$\map \Gamma {-\dfrac 1 2} = -2 \sqrt \pi$

where $\Gamma$ denotes the Gamma function.

## Proof

 $\ds \map \Gamma {-\dfrac 1 2}$ $=$ $\ds \frac {\map \Gamma {\frac 1 2} } {-1/2}$ Gamma Difference Equation $\ds$ $=$ $\ds -2 \, \map \Gamma {\frac 1 2}$ $\ds$ $=$ $\ds -2 \sqrt \pi$ Gamma Function of One Half

$\blacksquare$