• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 03/10/2009, 03:34 PM (This post was last modified: 03/10/2009, 03:49 PM by Ivars.) Based on what I found here: Entropy of Log-Poisson process The distribution of values including far rare jumps based on change of sign with mod under logarithm has to be log-Poisson or negative log-Poisson, because the mean value of such infinite iteration is entropy of such process $S= -\Omega$. Unofortunately, I could not find the parameters of log-Poisson distribution (mean, variance, skewness, kurtosis etc.) to compare with my numeric results. The hidden mean of 2 such distributions, log Poisson and negative log Poisson is $e^{+\Omega}= 1,7632..= 1/\Omega$ and $e^{-\Omega}= \Omega=0,567143..$ Ivars « Next Oldest | Next Newest »

 Messages In This Thread Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 03/25/2008, 10:36 PM RE:Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega for all x - by Ivars - 03/25/2008, 10:45 PM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 03/26/2008, 11:51 AM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by bo198214 - 03/27/2008, 09:29 AM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 04/02/2008, 09:44 PM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 03/27/2008, 03:38 PM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 04/06/2008, 11:45 AM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 04/06/2008, 06:14 PM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 04/06/2008, 06:55 PM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 03/10/2009, 03:34 PM RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by tommy1729 - 03/29/2015, 08:02 PM

 Possibly Related Threads... Thread Author Replies Views Last Post [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 14 5,855 12/13/2019, 02:33 PM Last Post: Ember Edison Math overflow question on fractional exponential iterations sheldonison 4 4,799 04/01/2018, 03:09 AM Last Post: JmsNxn Periodic analytic iterations by Riemann mapping tommy1729 1 2,653 03/05/2016, 10:07 PM Last Post: tommy1729 Dangerous limits ... Tommy's limit paradox tommy1729 0 2,191 11/27/2015, 12:36 AM Last Post: tommy1729 tetration limit ?? tommy1729 40 55,274 06/15/2015, 01:00 AM Last Post: sheldonison Another limit tommy1729 0 1,841 03/18/2015, 06:55 PM Last Post: tommy1729 A limit exercise with Ei and slog. tommy1729 0 2,196 09/09/2014, 08:00 PM Last Post: tommy1729 [MSE] The mick tommy limit conjecture. tommy1729 1 2,957 03/30/2014, 11:22 PM Last Post: tommy1729 regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,675 06/25/2013, 01:37 PM Last Post: sheldonison tetration base conversion, and sexp/slog limit equations sheldonison 44 62,813 02/27/2013, 07:05 PM Last Post: sheldonison

Users browsing this thread: 1 Guest(s)