• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 tetration limit ?? sheldonison Long Time Fellow Posts: 663 Threads: 23 Joined: Oct 2008 06/15/2015, 01:00 AM (This post was last modified: 06/15/2015, 03:07 AM by sheldonison.) (06/11/2015, 10:27 AM)sheldonison Wrote: .... $\lim\limits_{n\to\infty} \text{sexp}_{(\eta+1/n)}\left[\pi\sqrt{\frac{2\eta\cdot n}{e}} + \text{slog}_e(\frac{n}{e}-1) + C + \mathcal{O}(\theta) \right] -n = 0\;\;\;\;C \approx -2 - \text{slog}_e(388.7874/e-1)$$\lim\limits_{n\to\infty} \text{sexp}_{(\eta+1/n)}\left[\pi\sqrt{\frac{2\eta\cdot n}{e}} -2 \right] \approx 388.7874$ I was about to post a closely related question about Pi in the Mandelbrot set; it takes about $\pi \sqrt{n}$ iterations to escape near the parabolic cusp at c=0.25. Then I found this paper about the occurrence of Pi in the Mandelbrot set; although I haven't finished reading their paper, but I am sure the same mechanisms can be used to justify the result, that it takes $\pi \sqrt{\frac{2\eta \cdot n}{e}}$ iterations to "escape" for sexp_{eta+1/n}, and for iterating $z \mapsto \exp(z)-1+\frac{1}{n}$, it takes $\pi\sqrt{2n}$ iterations. http://www.doc.ic.ac.uk/~jb/teaching/jmc...elbrot.pdf - Sheldon « 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 21 1,929 03/29/2021, 02:54 AM Last Post: JmsNxn Dangerous limits ... Tommy's limit paradox tommy1729 0 2,962 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 20,388 03/29/2015, 08:02 PM Last Post: tommy1729 Another limit tommy1729 0 2,548 03/18/2015, 06:55 PM Last Post: tommy1729 A limit exercise with Ei and slog. tommy1729 0 2,910 09/09/2014, 08:00 PM Last Post: tommy1729 [MSE] The mick tommy limit conjecture. tommy1729 1 3,946 03/30/2014, 11:22 PM Last Post: tommy1729 tetration base conversion, and sexp/slog limit equations sheldonison 44 81,356 02/27/2013, 07:05 PM Last Post: sheldonison Solve this limit Nasser 4 7,239 12/03/2012, 07:46 AM Last Post: Nasser (MSE) A limit- question concerning base-change Gottfried 0 3,355 10/03/2012, 06:44 PM Last Post: Gottfried a limit curiosity ? Pi/2 tommy1729 0 3,003 08/07/2012, 09:27 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)