• 2 Vote(s) - 3 Average
• 1
• 2
• 3
• 4
• 5
 Andrew Robbins' Tetration Extension jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 11/06/2007, 01:58 PM bo198214 Wrote:jaydfox Wrote:I will do some testing, but my hunch is that the series will still converge on the "correct" solution, despite your attempt to break the solution. Because the modification you made is convergent, it has no radius of convergence, and hence it does not introduce a "false" singularity.I am not sure what you mean by false singularity and false function, and how you would introduce a singularity somewhere. Despite I am very interested in the results you will come up with.Sorry, it's how I picture it in my head and hence how I describe it. If you substituted the terms for the power series of 1/(z-3) for k>n, then you will have introduced a singularity to the solution. The system you solve would NOT just consist of the n terms you calculated, but an infinite number of terms, the first n of which are determined by the solution to the system, the remaining for k>n being given as an initial condition. Therefore, it would have a singularity at z=3, a simple pole in fact. This is a "false singularity", because it was introduced artificially, i.e., it was not predicted by the convergence of the finite systems. In fact, I would predict that convergence would nonetheless be to a series with singularities at the upper and lower fixed points (for base e). Quote:I also would suggest to stop calling one solution as being "correct" (as it doesnt fit the meaning of the word), I rather would suggest to call the solution gotten by Andrew's method as being "natural". I call it correct in the sense that the system should converge on the same solution, regardless of whatever initial conditions we specify for k>n, so long as those initial conditions do not attempt to reduce the radius of convergence below that of the system solved with 0's for k>n. But we can call it "natural" as well. ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread Andrew Robbins' Tetration Extension - by bo198214 - 08/07/2007, 04:38 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/18/2007, 08:20 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/19/2007, 09:50 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/20/2007, 02:22 PM RE: Andrew Robbins' Tetration Extension - by andydude - 11/12/2007, 08:43 AM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 06/26/2009, 10:51 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 06/27/2009, 09:39 AM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 06/28/2009, 12:08 AM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/06/2007, 04:17 AM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/06/2007, 04:27 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/06/2007, 10:57 AM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/06/2007, 01:58 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/06/2007, 03:58 PM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/12/2007, 09:14 AM RE: Andrew Robbins' Tetration Extension - by andydude - 11/12/2007, 09:56 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/12/2007, 08:05 PM RE: Andrew Robbins' Tetration Extension - by andydude - 11/13/2007, 12:16 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/13/2007, 10:21 AM RE: Andrew Robbins' Tetration Extension - by andydude - 11/13/2007, 05:45 PM RE: Andrew Robbins' Tetration Extension - by Gottfried - 03/17/2008, 07:52 AM RE: Andrew Robbins' Tetration Extension - by Gottfried - 03/17/2008, 06:09 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 06/29/2009, 08:20 PM RE: Andrew Robbins' Tetration Extension - by andydude - 07/27/2009, 08:10 AM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/11/2009, 12:18 PM RE: Andrew Robbins' Tetration Extension - by jaydfox - 08/11/2009, 07:06 PM RE: Andrew Robbins' Tetration Extension - by jaydfox - 08/11/2009, 07:12 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/23/2009, 02:45 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/23/2009, 03:23 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/26/2009, 04:01 PM RE: Andrew Robbins' Tetration Extension - by andydude - 09/04/2009, 06:42 AM RE: Andrew Robbins' Tetration Extension - by Gottfried - 12/28/2009, 05:21 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/18/2016, 12:29 PM RE: Andrew Robbins' Tetration Extension - by Gottfried - 08/22/2016, 04:19 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Possible continuous extension of tetration to the reals Dasedes 0 1,673 10/10/2016, 04:57 AM Last Post: Dasedes Non-trivial extension of max(n,1)-1 to the reals and its iteration. MphLee 3 4,618 05/17/2014, 07:10 PM Last Post: MphLee extension of the Ackermann function to operators less than addition JmsNxn 2 4,737 11/06/2011, 08:06 PM Last Post: JmsNxn Tetration Extension to Real Heights chobe 3 7,045 05/15/2010, 01:39 AM Last Post: bo198214 Tetration extension for bases between 1 and eta dantheman163 16 22,292 12/19/2009, 10:55 AM Last Post: bo198214 Extension of tetration to other branches mike3 15 24,361 10/28/2009, 07:42 AM Last Post: bo198214 andrew slog tommy1729 1 3,910 06/17/2009, 06:37 PM Last Post: bo198214 Dmitrii Kouznetsov's Tetration Extension andydude 38 43,881 11/20/2008, 01:31 AM Last Post: Kouznetsov Hooshmand's extension of tetration andydude 9 11,941 08/14/2008, 04:48 AM Last Post: Danesh

Users browsing this thread: 1 Guest(s)