# Why does $\Gamma (x)\ne x!$ on $x\in\mathbb N$? [duplicate]

From what I understand the Gamma function was created to expand the factorial to the real number line (and complex plane). So why is it that $\Gamma(x)=(x-1)!$ and is not equal to $x!$, where transitioning from discrete to continuous is much simpler?
• In fact Gauss used $\Pi(n)=n!$ – MPW Mar 1 '18 at 0:57
• Mostly historical. $\Gamma$ and $\Pi$ each have their advantages and disadvantages. They're related by a $1/z$ or a $z$, but why introduce more notation than you need? – Robert Wolfe Mar 1 '18 at 0:59