File:SquareRootOfFactorial.png

Graphical representation of the Square root of factorial: functions $y\!=\! \mathrm{factorial}(x)=x!$, thin black line, and $y\!=\!\mathrm{factorial}^{1/2}(x)\!=\!\sqrt{\mathrm{factorial}}(x) \!=\!\sqrt{!\,}(x)$, thick red line, versus $x$.

For $x\!>\!1$ the relation below holds:


 * $\sqrt{!\,}\!\Big( \sqrt{!\,}(x) \Big)=x!$

Copyleft 2011 by Dmitrii Kouznetsov.