# Gamma Function of One Half/Proof 4

## Theorem

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

Its decimal expansion starts:

$\map \Gamma {\dfrac 1 2} = 1 \cdotp 77245 \, 38509 \, 05516 \, 02729 \, 81674 \, 83341 \, 14518 \, 27975 \ldots$

## Proof

 $\displaystyle \Gamma \left({\frac 1 2}\right)$ $=$ $\displaystyle \frac {0!} {2^0 0!} \sqrt \pi$ Gamma Function of Positive Half-Integer $\displaystyle$ $=$ $\displaystyle \sqrt \pi$ Factorial of Zero

$\blacksquare$