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 elementary superfunctions bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 03/27/2010, 10:27 PM (This post was last modified: 03/27/2010, 10:44 PM by bo198214.) (04/29/2009, 04:58 PM)bo198214 Wrote: What does mathematica say about $f(x)=\frac{x-1}{x+1}$? This is strictly increasing and has no real fixed point. (04/29/2009, 05:07 PM)Ansus Wrote: It gives $ F(x)=\frac{\left(-\frac{1}{2}-\frac{i}{2}\right)^x(i C-1) + \left(-\frac{1}{2}+\frac{i}{2}\right)^x(i C+1)}{\left(-\frac{1}{2}-\frac{i}{2}\right)^x(i+ C)+\left(-\frac{1}{2}+\frac{i}{2}\right)^x(i-C) }$ Well we can do better: $f^{\circ u}(z)=\frac{\cos(\frac{\pi}{4}u)z-\sin(\frac{\pi}{4}u) }{\sin(\frac{\pi}{4}u)z+\cos(\frac{\pi}{4}u)}$ more detailed information in this article To be complete I will also give Gottfried's solution for $f(z)=\frac{1}{z+1}$ which has two real fixed points at $\pm\frac{1}{2}\sqrt{5}-\frac{1}{2}$, and singularity at -1: $f^{\circ u}(z)=\frac{\operatorname{fib}_u-\operatorname{fib}_{u-1}z}{\operatorname{fib}_{u+1}-\operatorname{fib}_{u}z}$ $\operatorname{fib}_u=\frac{\phi^u-(1-\phi)^u}{\sqrt{5}}$ $\phi=\frac{1+\sqrt{5}}{2}$ « Next Oldest | Next Newest »

 Messages In This Thread elementary superfunctions - by bo198214 - 04/23/2009, 01:25 PM RE: elementary superfunctions - by bo198214 - 04/23/2009, 02:23 PM RE: elementary superfunctions - by bo198214 - 04/23/2009, 03:46 PM RE: elementary superfunctions - by tommy1729 - 04/27/2009, 11:16 PM RE: elementary superfunctions - by bo198214 - 04/28/2009, 08:33 AM RE: elementary superfunctions - by bo198214 - 03/27/2010, 10:27 PM RE: elementary superfunctions - by bo198214 - 04/18/2010, 01:17 PM RE: elementary superfunctions - by tommy1729 - 04/18/2010, 11:10 PM RE: elementary superfunctions - by bo198214 - 04/25/2010, 08:22 AM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 09:11 AM RE: elementary superfunctions - by bo198214 - 04/25/2010, 09:23 AM RE: elementary superfunctions - by bo198214 - 04/25/2010, 10:48 AM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 11:35 AM RE: elementary superfunctions - by bo198214 - 04/25/2010, 12:12 PM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 12:42 PM RE: elementary superfunctions - by bo198214 - 04/25/2010, 01:10 PM RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 01:52 PM Super-functions - by Kouznetsov - 05/11/2009, 02:02 PM [split] open problems survey - by tommy1729 - 04/25/2010, 02:34 PM RE: [split] open problems survey - by bo198214 - 04/25/2010, 05:15 PM

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