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 Derivative of exp^[1/2] at the fixed point? sheldonison Long Time Fellow Posts: 641 Threads: 22 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

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