• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Change of base formula for Tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/15/2007, 09:00 PM (This post was last modified: 08/15/2007, 09:02 PM by bo198214.) jaydfox Wrote:Essentially, if k is the number of terms at which we truncate the series expansion, then there is a non-zero radius for which the series is initially convergent (i.e., the root-test for terms 1 through k would all be less than 1). I dont understand a word. If you truncate the series, it is a polynomial and a polynomial is defined on the whole complex numbers, i.e. infinite radius of convergence. Quote:Regardless, if the proof has already been shown, then combined with my change of base formula, we now have a unique solution to tetration of bases greater than eta. As it appears to me your change of base formula works merely for base $b$ greater than $\eta$ and $a. But thats exactly the wrong direction. We need to change the base from $b\le\eta$ to $a>\eta$. Even if we had a proper change of base formula we need to check that it is consistent for change of bases smaller than $\eta$, i.e. that it transforms the already known unique solution for base $b\le\eta$ into the already known unique solution for base $a\le\eta$. If we had a change of base formula then we anyway dont need the converging solution for $b=\eta$ (via $e^x-1$), because we could simply compute that solution from a smaller base. Quote:By the way, for the reference to Ecalle, where can I get a copy, and more importantly, is there an English translation available? Not sure, I lent it from the library. There seems no translation into english. « Next Oldest | Next Newest »

 Messages In This Thread Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:39 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:41 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 08:38 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 08:53 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 04:34 PM RE: Change of base formula for Tetration - by bo198214 - 08/12/2007, 06:39 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:00 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:09 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:30 PM RE: Change of base formula for Tetration - by andydude - 08/13/2007, 02:47 PM RE: Change of base formula for Tetration - by andydude - 08/13/2007, 02:58 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 06:34 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 07:31 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 07:37 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 08:03 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 08:23 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 08:32 PM RE: Change of base formula for Tetration - by bo198214 - 08/15/2007, 09:36 AM RE: Change of base formula for Tetration - by jaydfox - 08/15/2007, 10:15 AM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 03:42 PM RE: Change of base formula for Tetration - by jaydfox - 08/15/2007, 11:29 PM RE: Change of base formula for Tetration - by jaydfox - 08/16/2007, 09:21 PM RE: Change of base formula for Tetration - by bo198214 - 08/16/2007, 09:32 PM RE: Change of base formula for Tetration - by jaydfox - 08/16/2007, 09:49 PM RE: Change of base formula for Tetration - by bo198214 - 08/16/2007, 09:53 PM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 03:51 AM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 06:24 AM RE: Change of base formula for Tetration - by bo198214 - 08/31/2007, 09:03 AM RE: Change of base formula for Tetration - by tommy1729 - 05/03/2009, 10:20 PM RE: Change of base formula for Tetration - by sheldonison - 05/05/2009, 11:21 AM RE: Change of base formula for Tetration - by tommy1729 - 05/05/2009, 12:19 PM RE: Change of base formula for Tetration - by sheldonison - 05/05/2009, 01:29 PM RE: Change of base formula for Tetration - by bo198214 - 05/05/2009, 01:37 PM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 04:11 AM Convergence of Jay's change of base formula - by bo198214 - 08/15/2007, 09:00 PM RE: Parabolic Iteration - by jaydfox - 08/15/2007, 09:19 PM RE: Parabolic Iteration - by bo198214 - 08/15/2007, 09:30 PM RE: Parabolic Iteration - by jaydfox - 08/15/2007, 11:41 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 08:17 AM RE: Parabolic Iteration - by jaydfox - 08/16/2007, 05:51 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 06:40 PM RE: Parabolic Iteration - by jaydfox - 08/16/2007, 09:47 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 10:07 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Complex Tetration, to base exp(1/e) Ember Edison 7 4,130 08/14/2019, 09:15 AM Last Post: sheldonison Recursive formula generating bounded hyper-operators JmsNxn 0 1,943 01/17/2017, 05:10 AM Last Post: JmsNxn Is bounded tetration is analytic in the base argument? JmsNxn 0 1,791 01/02/2017, 06:38 AM Last Post: JmsNxn Extrapolated Faá Di Bruno's Formula Xorter 1 2,724 11/19/2016, 02:37 PM Last Post: Xorter [2015] 4th Zeration from base change pentation tommy1729 5 7,309 03/29/2015, 05:47 PM Last Post: tommy1729 Conjecture on semi-exp base change [2015] tommy1729 0 2,117 03/24/2015, 03:14 PM Last Post: tommy1729 tetration base sqrt(e) tommy1729 2 4,076 02/14/2015, 12:36 AM Last Post: tommy1729 Explicit formula for the tetration to base $$e^{1/e}$$? mike3 1 3,618 02/13/2015, 02:26 PM Last Post: Gottfried tetration base > exp(2/5) tommy1729 2 3,861 02/11/2015, 12:29 AM Last Post: tommy1729 about power towers and base change tommy1729 7 10,065 05/04/2014, 08:30 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)