• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 slog(superfactorial(x)) = ? tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 11/14/2012, 08:30 PM (This post was last modified: 11/14/2012, 08:37 PM by tommy1729.) Define the superfactorial as superfactorial(x) = super!(x) and super!(x+1) = factorial(super!(x)) = super!(x)! Where the factorial is computed from the gamma function and super!(-oo) = 2 and super!(0) = 3. Now I wonder how slog(super!(x)) looks like for large real x ? We know from basechange and the fact that gamma grows faster than exp that slog(super!(x)) must be strictly increasing for x > y for some real y. I wonder how fast this is. Could it be O(x/ln(x)) ? or O(ln(x) sqrt(x)) ? I have no theoretical reasons to assume anything apart from lim sup slog(super!(x)) < 2x. I could make up some arguments for this or that based upon asymptotics of gamma , but formal analysis instead of dubious arguments seems not easy. There are superfunctions known of the factorial but we only need integer iterations for the general behaviour ... on the other hand maybe the other values are needed in some proof ... I wonder what you guys think. I was thinking about a plot , but im not sure how we do this since superfactorial grows faster than tetration !! Maybe this requires some sort of ' simplify ' ( as math apps and books call it ) *command* towards slog(super!(x)) for which i have no idea how to do it. It looks a bit like basechange , but to me it looks harder. I think this is intresting because it might learn us alot about iteration in general and slog in particular. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread slog(superfactorial(x)) = ? - by tommy1729 - 11/14/2012, 08:30 PM RE: slog(superfactorial(x)) = ? - by sheldonison - 11/15/2012, 06:34 PM RE: slog(superfactorial(x)) = ? - by tommy1729 - 11/17/2012, 11:47 PM RE: slog(superfactorial(x)) = ? - by tommy1729 - 06/02/2014, 11:29 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Some slog stuff tommy1729 15 10,955 05/14/2015, 09:25 PM Last Post: tommy1729 A limit exercise with Ei and slog. tommy1729 0 1,789 09/09/2014, 08:00 PM Last Post: tommy1729 A system of functional equations for slog(x) ? tommy1729 3 4,073 07/28/2014, 09:16 PM Last Post: tommy1729 [stuck] On the functional equation of the slog : slog(e^z) = slog(z)+1 tommy1729 1 2,256 04/28/2014, 09:23 PM Last Post: tommy1729 A simple yet unsolved equation for slog(z) ? tommy1729 0 1,730 04/27/2014, 08:02 PM Last Post: tommy1729 A kind of slog ? C + SUM f_n(x) ln^[n](x) ? tommy1729 1 2,218 03/09/2013, 02:46 PM Last Post: tommy1729 tetration base conversion, and sexp/slog limit equations sheldonison 44 50,828 02/27/2013, 07:05 PM Last Post: sheldonison A support for Andy's (P.Walker's) slog-matrix-method Gottfried 0 2,280 11/14/2011, 04:01 AM Last Post: Gottfried Does anyone have taylor series approximations for tetration and slog base e^(1/e)? JmsNxn 18 19,942 06/05/2011, 08:47 PM Last Post: sheldonison Regular slog for base sqrt(2) - Using z=2 jaydfox 13 17,100 03/10/2010, 12:47 PM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)