Gamma Function of 2

Theorem

Let $\Gamma$ denote the Gamma function.

Then:

$\map \Gamma 2 = 1$

Proof

\(\ds \map \Gamma 2\)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 1 \map \Gamma 1\)

Gamma Difference Equation

\(\ds \)

\(=\)

\(\ds 1 \times 0!\)

Gamma Function Extends Factorial

\(\ds \)

\(=\)

\(\ds 1\)

Definition of Factorial: $0! = 1$

$\blacksquare$