Derivative of exp^[1/2] at the fixed point? sheldonison Long Time Fellow Posts: 684 Threads: 24 Joined: Oct 2008 12/23/2015, 04:39 PM (This post was last modified: 12/23/2015, 04:43 PM by sheldonison.) Let exp^[1/2](x) be the half iterate of exp(x), generated by Kneser's Riemann mapping. Is the derivative defined of exp^[1/2](L) defined at the fixed point of L~=0.318132 + 1.33724i, where exp(L)=L? From an old 2010 post#3..post#8 http://math.eretrandre.org/tetrationforu...4&pid=5400, we see that L is the closest singularity to the real axis for the half iterate, but it is a mild singularity, and that exp^[1/2](L)=L, so that exp^[1/2](L) is continuous at L. Is the derivative is also continuous at this singularity, and if so, then what is its value? If the derivative is continuous at the singularity, how many of the higher derivatives are also continuous? - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread Derivative of exp^[1/2] at the fixed point? - by sheldonison - 12/23/2015, 04:39 PM RE: Derivative of exp^[1/2] at the fixed point? - by sheldonison - 12/24/2015, 03:25 AM RE: Derivative of exp^[1/2] at the fixed point? - by sheldonison - 12/25/2015, 04:05 PM RE: Derivative of exp^[1/2] at the fixed point? - by andydude - 12/27/2015, 11:15 AM RE: Derivative of exp^[1/2] at the fixed point? - by sheldonison - 12/27/2015, 11:40 PM RE: Derivative of exp^[1/2] at the fixed point? - by andydude - 12/29/2015, 10:51 PM RE: Derivative of exp^[1/2] at the fixed point? - by sheldonison - 12/29/2015, 10:25 PM RE: Derivative of exp^[1/2] at the fixed point? - by sheldonison - 12/31/2015, 11:02 AM RE: Derivative of exp^[1/2] at the fixed point? - by tommy1729 - 12/31/2015, 01:25 PM RE: Derivative of exp^[1/2] at the fixed point? - by sheldonison - 01/01/2016, 03:58 PM RE: Derivative of exp^[1/2] at the fixed point? - by tommy1729 - 12/30/2015, 01:27 PM

 Possibly Related Threads… Thread Author Replies Views Last Post Iteration with two analytic fixed points bo198214 62 6,311 11/27/2022, 06:53 AM Last Post: JmsNxn The Different Fixed Points of Exponentials Catullus 22 2,425 07/24/2022, 12:22 PM Last Post: bo198214 Quick way to get the repelling fixed point from the attracting fixed point? JmsNxn 10 1,306 07/22/2022, 01:51 AM Last Post: JmsNxn Apropos "fix"point: are the fractional iterations from there "fix" as well? Gottfried 12 1,509 07/19/2022, 03:18 AM Last Post: JmsNxn Two Attracting Fixed Points Catullus 4 661 07/04/2022, 01:04 PM Last Post: tommy1729 Derivative of the Tetration Logarithm Catullus 1 495 07/03/2022, 07:23 AM Last Post: JmsNxn On the first derivative of the n-th tetration of f(x) Luknik 5 1,943 10/28/2021, 11:53 AM Last Post: tommy1729 tetration from alternative fixed point sheldonison 22 59,954 12/24/2019, 06:26 AM Last Post: Daniel Semi-exp and the geometric derivative. A criterion. tommy1729 0 3,516 09/19/2017, 09:45 PM Last Post: tommy1729 How to find the first negative derivative ? tommy1729 0 3,540 02/13/2017, 01:30 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)