Thread Rating:
• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 [Update] Comparision of 5 methods of interpolation to continuous tetration tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 10/28/2013, 11:11 PM Ok some guts is needed to admit I do not fully understand and to say I find some things not perfectly well explained. In particular because it sounds stupid and ungrateful , which I am not. But it needs to be done. For Kneser's solution alot of attention is going to the Riemann mapping but the " a priori " is not clear to me. Maybe Im getting old and I am asking question that I have asked before or understood before so plz forgive me if so. From my experience it is best to ask very specific questions so I will point to the post I find most confusing. But first a silly question probably , what I will probably know right after I asked :p About the schroeder equation F( f(x) ) = q F(x). Let c be the fixpoint of f(x). Now it appears to me that F© must be either 0 or infinite. What usefull stuff can be said if F© = oo ? Or is that completely useless ? Second , Why do we prefer f ' © = 1 ? I assume it is ONLY for the easy solvability of the Taylor series or limit formula for the " principal " schroeder function. Having probably answered those questions somewhat myself , let continue with the MAIN question(s) and the principal schroeder function. Since we have f © = 0 we thus have a Taylor series expanded at c. However there is a limit radius of convergence. And the real line is not included in the radius , so the trouble begins. I was only able to find ONE POST adressing how to continue before the Riemann mapping ( all the others seemed to be copied or linked to that " mother post " ) It is still not clear to me what exactlty is mapped , what happened to the singularities and if all that does not loose the property of analyticity. Also Im not sure what kind of " solution " we are suppose to end up with ?? A sexp that has no singularities for Re > 0 ? What properties are claimed for the Kneser solution ? Is it only the property of sexp being analytic near the real line for Re > 0 ? The post that failed to enlighten me was this one : - with respect to the poster of course - http://math.eretrandre.org/tetrationforu...hp?tid=213 POST NR 3 It is said : we analyticly continue to ... HOW ? What happened to the singularities and limited radius ? If you use Taylor series you CANNOT have a function that converges on the entire upper plane ; the Taylor series ALWAYS converges in a circle !!? It is not said how the continuation is done , how we know it is possible , what series expansion we end up with etc etc So what to make of that ? I note that mapping a singularity or pole with exp or ln remains a problem ? Then there follows a claim of simply connected which I find a bit handwaving ?? And what if it contains singularities ?? How is this different from Gottfriend's brown curve ? I also note that the Riemann mapping may not change the functional equation. Those 3 pics do not explain all that and perhaps a longer post should have been made. With respect to the efforts though. I hope I have sketched what I believe confuses most people about Kneser's method. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/13/2013, 02:20 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by MikeSmith - 10/14/2013, 10:42 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/14/2013, 01:19 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by MikeSmith - 10/14/2013, 08:22 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 12:59 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/14/2013, 10:07 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 12:00 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 01:09 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/15/2013, 07:14 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 11:14 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/16/2013, 12:54 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/16/2013, 04:12 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/16/2013, 05:07 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/22/2013, 12:17 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/22/2013, 01:53 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/27/2013, 11:40 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/28/2013, 04:17 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/28/2013, 11:11 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/28/2013, 11:29 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/29/2013, 09:37 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/28/2013, 11:32 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/29/2013, 01:11 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/29/2013, 02:52 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 11/01/2013, 02:16 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/01/2014, 12:09 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/04/2014, 12:31 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 02/03/2014, 01:13 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/03/2014, 01:44 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/03/2014, 01:59 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 02/03/2014, 10:35 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/03/2014, 11:07 PM

 Possibly Related Threads... Thread Author Replies Views Last Post My interpolation method [2020] tommy1729 1 303 02/20/2020, 08:40 PM Last Post: tommy1729 Possible continuous extension of tetration to the reals Dasedes 0 1,497 10/10/2016, 04:57 AM Last Post: Dasedes Tribonacci interpolation ? tommy1729 0 2,088 09/08/2014, 10:37 AM Last Post: tommy1729 How many methods have this property ? tommy1729 1 2,741 05/22/2014, 04:56 PM Last Post: sheldonison (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 2,064 05/22/2013, 07:02 AM Last Post: Gottfried [UFO] - a contradiction in assuming continuous tetration? Gottfried 18 22,365 08/29/2010, 08:44 PM Last Post: Gottfried Self tetraroot constructed via Newton series interpolation mike3 2 6,877 07/11/2010, 03:38 AM Last Post: mike3 Borel summation and other continuation/summability methods for continuum sums mike3 2 5,517 12/30/2009, 09:51 PM Last Post: mike3 A false interpolation paradigm (?); a reconsideration Gottfried 4 7,733 09/17/2009, 08:17 AM Last Post: bo198214 exponential polynomial interpolation Gottfried 3 7,352 07/16/2008, 10:32 PM Last Post: andydude

Users browsing this thread: 1 Guest(s)