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 tetration limit ?? tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 04/02/2009, 10:39 PM 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: $\lim_{n\to\infty} (1+f(n))^{(1+f(n))^{n}} = Q$ 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 « Next Oldest | Next Newest »

 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 Updated results for tetration limit - by sheldonison - 10/31/2010, 03:32 PM 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

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