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 tetration limit ?? tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 04/30/2009, 11:38 PM BenStandeven Wrote:Let's see here. The fixed point for base (eta + eps) is e + delta(eps), where delta satisfies: $[1/e + \ln(1 + \eps/\eta)] (e + \delta(\eps)) = 1 + \ln(1 + \delta(\eps)/e)$ $[1/e + \eps/\eta + O(eps^2)] (e + \delta(\eps)) = 1 + \ln(1 + \delta(\eps)/e)$ $[\eps/\eta + O(\eps^2)] (e + \delta(\eps)) = -(\delta(\eps)/e)^2/2 + O(\delta(\eps)^3)$ So $\delta(\eps) \approx \sqrt{\eps}$ and $0 = e\eps/\eta + \delta(\eps) \eps/\eta + (\delta(\eps)/e)^2/2 + O((\eps)^{3/2}$ $\delta(\eps) = \frac{ - \eps/\eta + \sqrt{ \eps^2/\eta^2 - \frac{2 \eps}{e \eta} } } { 1/e^2 } + O(\eps^{3/2})$ $\delta(\eps) = \frac{ - \eps/\eta + \sqrt{\frac{-2 \eps}{e \eta}} [1 - \frac{e \eps}{4 \eta} + O(\eps^2)] } { 1/e^2 } + O(\eps^{3/2})$ $\delta(\eps) = -e^2 \eps/\eta + \sqrt{2/\eta} e^{3/2} \sqrt{-\eps} + O(\eps^{3/2})$ euh i dont mean to be rude , but euh , where is the limit ? this thread is about a limit , so whatever you wrote may be brilliant , but i dont know what you mean or if you talk about the same thing ? 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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