• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 fractional iteration by schröder and by binomial-formula Gottfried Ultimate Fellow Posts: 789 Threads: 121 Joined: Aug 2007 11/23/2011, 04:45 PM (This post was last modified: 11/23/2011, 04:49 PM by Gottfried.) Just a small result from some playing around in a break; I'll look at the confirmation for a wider range of parameters later. This days I'm re-considering the differences of the fractional iterates of $b^x -1$ using the schröder-function by their carleman-matrices. At the moment I use b=2, comparing the results when I use the power series centered around fixpoint t0=0 versus that around fixpoint t1=1. The range of 01. The point x0, at which the most symmetric sinusoidal curve occurs seems to be x0~0.382160520000... (not rational!) which has a special property for base b=2 which I'll discuss in a later post. Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread fractional iteration by schröder and by binomial-formula - by Gottfried - 11/23/2011, 04:45 PM

 Possibly Related Threads... Thread Author Replies Views Last Post On my old fractional calculus approach to hyper-operations JmsNxn 14 3,768 07/07/2021, 07:35 AM Last Post: JmsNxn [exercise] fractional iteration of f(z)= 2*sinh (log(z)) ? Gottfried 4 1,943 03/14/2021, 05:32 PM Last Post: tommy1729 There is a non recursive formula for T(x,k)? marraco 5 3,139 12/26/2020, 11:05 AM Last Post: Gottfried Math overflow question on fractional exponential iterations sheldonison 4 9,485 04/01/2018, 03:09 AM Last Post: JmsNxn Recursive formula generating bounded hyper-operators JmsNxn 0 3,335 01/17/2017, 05:10 AM Last Post: JmsNxn Extrapolated Faá Di Bruno's Formula Xorter 1 4,551 11/19/2016, 02:37 PM Last Post: Xorter Explicit formula for the tetration to base $$e^{1/e}$$? mike3 1 5,564 02/13/2015, 02:26 PM Last Post: Gottfried [MSE] Fixed point and fractional iteration of a map MphLee 0 3,850 01/08/2015, 03:02 PM Last Post: MphLee Fractional calculus and tetration JmsNxn 5 12,959 11/20/2014, 11:16 PM Last Post: JmsNxn Theorem in fractional calculus needed for hyperoperators JmsNxn 5 12,031 07/07/2014, 06:47 PM Last Post: MphLee

Users browsing this thread: 1 Guest(s)