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?
Asked
Active
Viewed 40 times
0
-
In fact Gauss used $\Pi(n)=n!$ – MPW Mar 01 '18 at 00:57
-
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? – Mar 01 '18 at 00:59