File:AbelFactorialR.png

$y=\mathrm{ArcFactorial}(x)$, dashed, and $y=\mathrm{AbelFactorial}(x)$, solid versus real $x$.

Arcfactorial is inverse function of Factorial

AbelFactorial is inverse function of SuperFactorial, AbelFactorial $G$ is solution of the Abel equation
 * $G(z!)=G(z)+1$