Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
tetration limit ??
#7
bo198214 Wrote:
tommy1729 Wrote:n is an integer

F [( 1 + f(n) ) ; F [( 1 + f(n) ) ; n ] ] = (1 + f(n) ) ^ n


F has two arguments seperated by " ; " and has the form
F[ base ; z ] and is the half iterate of base ^ z.

Perhaps then you should start with the simpler case of the double iterate. And look what a suitable function f you would find that:


I dont see what useful function f that could be.

first of all , i have to comment that i find you are changing subject a little bit.

what you call a simpler case might be a harder case or an unrelated case.

no offense.

( i think your limit like question is to " sensitive ". i wont explain that )

but i will try to give it a go anyways ...

(1 + f(n)) ^ (1 + f(n)) ^ n = Q

i try to use the identity lim (1 + 1 / g(n)) ^ g(n) = e

( for many g(n) )

so : 1 + 1/ ((1 + f(n)) ^n) = 1 + f(n)

so f(n) = (1 + f(n)) ^ - n

which leads to

f(z) = ( 1 + f(z) ) ^ - z

and Q = e


... maybe ...


however note that ( 1 + 1/n + 1/n^3 ) ^ n = e too , so some flexibility can be added to the equation for f(z) ...


at first sight id estimate f(z) around a / log(z) + b/ log(z)^c for some reals a, b and c.


another method might be taking the log of both sides getting an expression for log(Q) and then using l'hospital.

maybe that is more succesfull.

maybe both give a working result but different !?!

this might be bo's objection somewhat hidden.

but i dont think such an issue occurs in my OP.


( informally : in general limits with double exponential speed tends to converge to a finite numbers less then limits of slower functions )

regards

tommy1729
Reply


Messages In This Thread
tetration limit ?? - by tommy1729 - 04/01/2009, 05:49 PM
RE: tetration limit ?? - by nuninho1980 - 04/01/2009, 08:15 PM
RE: tetration limit ?? - by bo198214 - 04/02/2009, 09:58 PM
RE: tetration limit ?? - by nuninho1980 - 04/03/2009, 12:53 AM
RE: tetration limit ?? - by bo198214 - 04/03/2009, 12:49 PM
RE: tetration limit ?? - by nuninho1980 - 04/03/2009, 05:54 PM
RE: tetration limit ?? - by bo198214 - 04/02/2009, 02:50 PM
RE: tetration limit ?? - by tommy1729 - 04/02/2009, 09:24 PM
RE: tetration limit ?? - by bo198214 - 04/02/2009, 09:56 PM
RE: tetration limit ?? - by tommy1729 - 04/02/2009, 10:39 PM
RE: tetration limit ?? - by tommy1729 - 05/29/2011, 07:28 PM
RE: tetration limit ?? - by bo198214 - 05/31/2011, 10:34 AM
RE: tetration limit ?? - by nuninho1980 - 04/03/2009, 06:12 PM
RE: tetration limit ?? - by bo198214 - 04/06/2009, 10:49 PM
RE: tetration limit ?? - by nuninho1980 - 04/07/2009, 01:35 AM
RE: tetration limit ?? - by nuninho1980 - 04/04/2009, 02:21 PM
RE: tetration limit ?? - by gent999 - 04/14/2009, 10:12 PM
RE: tetration limit ?? - by bo198214 - 04/14/2009, 10:31 PM
RE: tetration limit ?? - by gent999 - 04/15/2009, 12:18 AM
RE: tetration limit ?? - by bo198214 - 04/15/2009, 01:35 PM
RE: tetration limit ?? - by tommy1729 - 04/15/2009, 03:05 PM
RE: tetration limit ?? - by gent999 - 04/15/2009, 04:41 PM
RE: tetration limit ?? - by tommy1729 - 04/29/2009, 01:08 PM
RE: tetration limit ?? - by BenStandeven - 04/30/2009, 11:29 PM
RE: tetration limit ?? - by tommy1729 - 04/30/2009, 11:38 PM
RE: tetration limit ?? - by BenStandeven - 05/01/2009, 01:35 AM
RE: tetration limit ?? - by BenStandeven - 05/01/2009, 01:00 AM
RE: tetration limit ?? - by JmsNxn - 04/14/2011, 08:17 PM
RE: tetration limit ?? - by tommy1729 - 05/28/2011, 12:28 PM
RE: tetration limit ?? - by nuninho1980 - 10/31/2010, 10:31 PM
RE: tetration limit ?? - by JmsNxn - 05/29/2011, 02:06 AM
RE: tetration limit ?? - by tommy1729 - 05/14/2015, 08:29 PM
RE: tetration limit ?? - by tommy1729 - 05/14/2015, 08:33 PM
RE: tetration limit ?? - by tommy1729 - 05/28/2015, 11:32 PM
RE: tetration limit ?? - by sheldonison - 06/11/2015, 10:27 AM
RE: tetration limit ?? - by sheldonison - 06/15/2015, 01:00 AM
RE: tetration limit ?? - by tommy1729 - 06/01/2015, 02:04 AM
RE: tetration limit ?? - by tommy1729 - 06/11/2015, 08:25 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Dangerous limits ... Tommy's limit paradox tommy1729 0 1,770 11/27/2015, 12:36 AM
Last Post: tommy1729
  Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x Ivars 10 13,958 03/29/2015, 08:02 PM
Last Post: tommy1729
  Another limit tommy1729 0 1,465 03/18/2015, 06:55 PM
Last Post: tommy1729
  A limit exercise with Ei and slog. tommy1729 0 1,824 09/09/2014, 08:00 PM
Last Post: tommy1729
  [MSE] The mick tommy limit conjecture. tommy1729 1 2,424 03/30/2014, 11:22 PM
Last Post: tommy1729
  tetration base conversion, and sexp/slog limit equations sheldonison 44 51,717 02/27/2013, 07:05 PM
Last Post: sheldonison
  Solve this limit Nasser 4 4,418 12/03/2012, 07:46 AM
Last Post: Nasser
  (MSE) A limit- question concerning base-change Gottfried 0 2,249 10/03/2012, 06:44 PM
Last Post: Gottfried
  a limit curiosity ? Pi/2 tommy1729 0 1,952 08/07/2012, 09:27 PM
Last Post: tommy1729
  Question about tetration limit mike3 3 5,057 07/13/2011, 12:51 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)