Gamma Function of Zero

Theorem

Let $\Gamma$ denotes the Gamma function

Then:

$\map \Gamma 0$ is not defined.

$\ds \map \Gamma 1$

$=$

$\ds 0 \, \map \Gamma 0$

$\ds \leadsto \ \ $

$\ds \map \Gamma 0$

$=$

$\ds \dfrac {\map \Gamma 1} 0$

$\ds $

$=$

$\ds \dfrac 1 0$

But $\dfrac 1 0$ is not defined.

Hence the result.

$\blacksquare$

1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Solved Problems: The Gamma Function: $33 \ \text{(d)}$