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 Uniqueness of half-iterate of exp(x) ? hixidom Junior Fellow Posts: 20 Threads: 3 Joined: Feb 2014 05/08/2014, 07:39 PM (This post was last modified: 05/08/2014, 08:11 PM by hixidom.) Ahhh. Thank you. That makes a lot of sense. I assume b is a constant, then I solve for b as a function of x! I am pretty dense. Anyways, here's something else I found that may be of use, Let's say that $f(x)=e^{g(x)}$. Then by definition $f(f(x))=e^{g(e^{g(x)})}=e^x\\\Rightarrow g(e^{g(x)})=x\\\Rightarrow e^{g(x)}=g^{-1}(x)$ Now substitute g(x) for x, $e^{g(g(x))}=g^{-1}(g(x))=x\\\Rightarrow g(g(x))=ln(x)$ So, in conclusion, the half-iterate of e^x is the exponential of the half-iterate of ln(x). Not sure if that is useful but I think it's kinda neat. Hopefully I didn't make another mistake, but it's always possible. « Next Oldest | Next Newest »

 Messages In This Thread Uniqueness of half-iterate of exp(x) ? - by tommy1729 - 03/21/2014, 11:55 PM RE: Uniqueness of half-iterate of exp(x) ? - by tommy1729 - 03/26/2014, 01:26 PM RE: Uniqueness of half-iterate of exp(x) ? - by tommy1729 - 03/27/2014, 11:23 PM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 12:57 AM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 05/08/2014, 05:28 AM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 07:31 AM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 05/08/2014, 01:49 PM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 04:28 PM RE: Uniqueness of half-iterate of exp(x) ? - by jaydfox - 05/08/2014, 07:04 PM RE: Uniqueness of half-iterate of exp(x) ? - by jaydfox - 05/08/2014, 07:24 PM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 07:39 PM RE: Uniqueness of half-iterate of exp(x) ? - by Xorter - 01/07/2017, 11:00 PM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 01/08/2017, 01:31 AM RE: Uniqueness of half-iterate of exp(x) ? - by Xorter - 01/08/2017, 10:55 AM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 01/09/2017, 02:41 AM

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