• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 tetration limit ?? BenStandeven Junior Fellow Posts: 27 Threads: 3 Joined: Apr 2009 05/01/2009, 01:33 AM BenStandeven Wrote:BenStandeven Wrote:Let's see here. The fixed point for base (eta + eps) is e + delta(eps), where delta satisfies: $\delta(\eps) = -e^2 \eps/\eta + \sqrt{2/\eta} e^{3/2} \sqrt{-\eps} + O(\eps^{3/2})$ $(\eta + \eps)^{e + \Re(\delta(\eps)) + \theta} = e^{1 + \theta (1 + e \eps/\eta)/e} + O(\eps^{3/2})$ Now if $\theta$ is on the order of $\sqrt \eps$, we have $(\eta + \eps)^{e + \Re(\delta(\eps)) + \theta} = e + \theta + \theta^2/2e + O(\eps^{3/2})$, so the effect of an additional level of tetration is to add $-\Re(\delta(\eps)) + \theta^2/2e$ to the exponent. To cross this region of length $2 \sqrt \eps$ would require between $2 / (\sqrt \eps (e^2/\eta + 1/2e))$ and $2 / (\sqrt \eps (e^2/\eta))$ steps. But if $\theta$ is of a larger order, the epsilon-dependent terms may be neglected, and we get that $(\eta + \eps)^{e + \theta} = \eta^{e + \theta} + O(\eps)}$. So it takes roughly $slog_{\eta}(e - \sqrt\eps)$ tetration levels to reach $e - \sqrt \eps$. To be continued... « 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

 Possibly Related Threads... Thread Author Replies Views Last Post Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 9,092 05/26/2021, 11:55 PM Last Post: MphLee Dangerous limits ... Tommy's limit paradox tommy1729 0 3,575 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 23,401 03/29/2015, 08:02 PM Last Post: tommy1729 Another limit tommy1729 0 3,080 03/18/2015, 06:55 PM Last Post: tommy1729 A limit exercise with Ei and slog. tommy1729 0 3,495 09/09/2014, 08:00 PM Last Post: tommy1729 [MSE] The mick tommy limit conjecture. tommy1729 1 4,750 03/30/2014, 11:22 PM Last Post: tommy1729 tetration base conversion, and sexp/slog limit equations sheldonison 44 95,229 02/27/2013, 07:05 PM Last Post: sheldonison Solve this limit Nasser 4 8,632 12/03/2012, 07:46 AM Last Post: Nasser (MSE) A limit- question concerning base-change Gottfried 0 4,001 10/03/2012, 06:44 PM Last Post: Gottfried a limit curiosity ? Pi/2 tommy1729 0 3,548 08/07/2012, 09:27 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)