Gamma Function of One Half/Proof 4

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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

$\blacksquare$