tetration limit ??

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tetration limit ??

tommy1729 $Offline$
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Posts: 1,354
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#23

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

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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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