• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Iterability of exp(x)-1 jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 08/12/2007, 04:41 PM (This post was last modified: 08/12/2007, 04:46 PM by jaydfox.) bo198214 Wrote:Inspired by JaydFox mentioning P. L. Walker (which I didnt have heard of before) I just read the abstract of his paper [1]: Quote:The author considers the Abel functional equation $g(\varphi(x))=g(z)+1$, where $\varphi$ is a given entire function and $g$ is an unknown entire function to be found. The inverse function $f=g^{-1}$ (if one exists) must satisfy (1) $f(w+1)=\varphi(f(w))$. The purpose of this paper is to show that for a wide class of entire functions, which includes $\varphi(z)=e^z-1$, equation (1) has a nonconstant entire solution. So I guess some results of I. N. Baker are indeed errournous. [1] P. L. Walker, A class of functional equations which have entire solutions, Bull. Austral. Math. Soc. 38 (198, no. 3, 351-356I think that settles it. If $\varphi(z)=e^z-1$ has an entire solution, then the cheta function should define a unique solution for tetration. And with my exact formula for base conversion, we can solve all bases. I'll put together a consolidated post with all the necessarily formulae. Currently they are spread across separate posts (which is good, as this allows feedback on each portion of the solution). « Next Oldest | Next Newest »

 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

Users browsing this thread: 1 Guest(s)