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Iterability of exp(x)-1
#7
Now I indeed had a look at
Quote:[1] P. L. Walker, A class of functional equations which have entire solutions, Bull. Austral. Math. Soc. 38 (198Cool, no. 3, 351-356
but things become more complicated!
Lets starting with his theorem:
Quote:Theorem 2. Let be an entire function of the form , where for all , and either (i) or (ii) .
Then the sequence defined in Theorem 1 converges uniformly on every to a function which is an entire non-constant solution of (2).
Where (2) is . The also mentioned theorem 1 and sequence does not matter yet.

What however really bothers me, that it seems not to be true:
Let . This is a feasible function for theorem 2, with and .
Now I looked at the (unqiue) half iterate

which should be entire too, for comparison some members of its series:

and tested convergence at (an entire function has an infinite radius of convergence, so it should converge for every ) and what did I find? Divergence!
Quote:0, 5.0, 17.50000000, -13.75000000, 142.5000000, -834.0625000, 5757.734375, -38187.57812, 222737.7149, -830118.7301, -3591005.876, 123831803.7, -1672085945.

So it seems this proof is also not reliable...
Boy that shakes my trust in professional mathematics.
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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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