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Iterability of exp(x)-1
#1
Hm, this is strange. I just tried numerically the half iterate of and it looks quite convergent.
However I read in the article of Erdös and Jabotinsky [1]:
Quote:The function was shown by I. N. Baker [2] to have no real non-integer iterates. M. Levine [3] showed, using some results of the present paper, that this function and the functions and have no analytic iterate.

Now I am confused. If someone wants to compare, I computed the half iterate of to be
I verified that indeed and it converges for example for
Code:
1.0,1.250000000,1.270833333,1.270833333,1.271093750,1.271017795,1.271019345,1.271034749,1.271025674,1.271025591,1.271029198,1.271027503

Where is the mistake?

[1] P. Erdös and E. Jabotinksy, On analytic iteration, J. Analyse Math. 8, 1960/1961, 361-376.
[2] I. N. Baker, Zusammensetzungen ganzer Funktionen, Math. Z 69, 1958, 121-163.
[3] M. Levin, MSc. Thesis, Israel Institute of Technology, 1960.
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Messages In This Thread
Iterability of exp(x)-1 - by bo198214 - 08/11/2007, 09:33 PM
RE: Iterability of exp(x)-1 - by Daniel - 08/11/2007, 09:49 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/11/2007, 11:42 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/12/2007, 09:07 AM
RE: Iterability of exp(x)-1 - by jaydfox - 08/12/2007, 04:41 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 08:54 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/11/2007, 10:25 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 09:06 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 09:13 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 09:16 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 09:33 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 10:00 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:05 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 10:11 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:22 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:00 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/13/2007, 10:29 PM
RE: Iterability of exp(x)-1 - by andydude - 08/13/2007, 10:30 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/13/2007, 10:39 PM
RE: Iterability of exp(x)-1 - by andydude - 08/15/2007, 08:36 AM
RE: Iterability of exp(x)-1 - by bo198214 - 08/15/2007, 09:21 AM
RE: Iterability of exp(x)-1 - by andydude - 08/15/2007, 08:40 PM
RE: Iterability of exp(x)-1 - by jaydfox - 08/15/2007, 08:54 AM
RE: Iterability of exp(x)-1 - by jaydfox - 08/15/2007, 08:53 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/15/2007, 09:13 PM
RE: Iterability of exp(x)-1 - by bo198214 - 08/20/2007, 04:14 PM
RE: Iterability of exp(x)-1 - by andydude - 09/05/2007, 08:15 PM
RE: Iterability of exp(x)-1 - by bo198214 - 09/07/2007, 02:45 PM
RE: Iterability of exp(x)-1 - by Gottfried - 03/15/2008, 09:13 AM
RE: Iterability of exp(x)-1 - by bo198214 - 03/15/2008, 01:14 PM
RE: Iterability of exp(x)-1 - by Gottfried - 03/15/2008, 08:25 PM
RE: Iterability of exp(x)-1 - by Gottfried - 03/18/2008, 10:14 AM



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