Gamma Function of 3

Theorem

Let $\Gamma$ denote the Gamma function.

Then:

$\map \Gamma 3 = 2$

Proof

\(\ds \map \Gamma 3\)

\(=\)

\(\ds \map \Gamma {2 + 1}\)

\(\ds \)

\(=\)

\(\ds 2 \map \Gamma 2\)

Gamma Difference Equation

\(\ds \)

\(=\)

\(\ds 2 \times 1\)

Gamma Function of 2

$\blacksquare$