11/15/2012, 06:34 PM
(This post was last modified: 11/16/2012, 02:27 AM by sheldonison.)

(11/14/2012, 08:30 PM)tommy1729 Wrote: Define the superfactorial as superfactorial(x) = super!(x) andHey Tommy,

super!(x+1) = factorial(super!(x)) = super!(x)!

Interesting question, I'll post more later. The fixed point=2, super! has a well defined schroder and inverse schroder function. I think it comes down to how big is and it seems like its not going to be that much bigger than . So should converge to a constant for integer values of n. I would expect a constant plus a 1-cyclic function real values of n.

updateThe , for large enough x, the log(x) multiplier term becomes arbitrarily accurate. .

The important thing is that slog((x+1)log(x)), if x is big enough, approaches arbitrarily close slog(x), so slog(super!(n))-n approaches a constant as n increases.

- Sheldon