Thread Rating:
• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 (UFO) Recentering and Schroeder function Gottfried Ultimate Fellow Posts: 757 Threads: 116 Joined: Aug 2007 06/10/2011, 06:57 PM (This post was last modified: 12/10/2012, 10:38 PM by Gottfried.) It may be a bit bizarre that I ask this question two or three years after I learned the use of the schroederfunction and the recentering of the powerseries for the purpose of fractional iteration... Well the question surfaces just after looking at my sketchpad, where I've written the recentering-formalism for the powerseries and the schroeder-function together. We have for some function f(x), recentered at fixpoint t the iterable decomposition into Schroederfunctions, depending on the iteration-height h and the eigenvalue u: $f^{[h]}(t) = t+ \sigma^{-1} ( u^h * \sigma (x-t) )$ When I look at this I ask how it was justified to use the schroeder-functions with only partly recentering; shouldn't we expect: $f^{[h]}(t) = t+ \sigma^{-1} \left( u^h * \left(t+ \sigma (x-t) \right) -t \right) = t+ \sigma^{-1} \left( t (u^h-1)+ u^h \sigma (x-t) \right)$ Always thinking in terms of the matrix-notations this seems more naturally to me (it is the similarity transformation). Well I've tried a quick check what would happen if I modified the standard computation this way and, as expected, I got salad. But why is this, that we allow to use the schroeder-function in context with a centered series where the centering is included only partly? (I have the article of Schroeder where he explains his method but don't remember (I'll look at it) that he was explicitely dealing with that recentering....) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Is there a function space for tetration? Chenjesu 0 267 06/23/2019, 08:24 PM Last Post: Chenjesu Degamma function Xorter 0 745 10/22/2018, 11:29 AM Last Post: Xorter Should tetration be a multivalued function? marraco 17 15,512 01/14/2016, 04:24 AM Last Post: marraco Introducing new special function : Lambert_t(z,r) tommy1729 2 3,365 01/10/2016, 06:14 PM Last Post: tommy1729 Tommy-Mandelbrot function tommy1729 0 1,831 04/21/2015, 01:02 PM Last Post: tommy1729 The inverse gamma function. tommy1729 3 7,284 05/13/2014, 02:18 PM Last Post: JmsNxn entire function close to sexp ?? tommy1729 8 8,949 04/30/2014, 03:49 PM Last Post: JmsNxn Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 6,546 07/17/2013, 09:46 AM Last Post: Gottfried Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 2,904 06/15/2013, 08:02 PM Last Post: MphLee Hyperzeta function Balarka Sen 7 7,623 05/08/2013, 01:36 PM Last Post: Balarka Sen

Users browsing this thread: 1 Guest(s)