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 elementary superfunctions Kouznetsov Fellow Posts: 151 Threads: 9 Joined: Apr 2008 04/25/2010, 09:11 AM (04/25/2010, 08:22 AM)bo198214 Wrote: Another one: $f(x)=x^2+(1+\sqrt{5})x+1$ $F(x)=e^{2^x} - \frac{1+\sqrt{5}}{2}$ $f$ has two fixed points with the derivations: $f'(\frac{1-\sqrt{5}}{2}) = 2$ and $f'(\frac{-1-\sqrt{5}}{2}) = 0$. The above superfunction $F$ is the regular iteration at the upper fixed point $\frac{1-\sqrt{5}}{2}$ Henryk, it seems to me that such a case can be obtained from the example 5 of the Table 1 of our article D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12 (English version), p.8-14 (Russian version; http://www.ils.uec.ac.jp/~dima/PAPERS/2009superfae.pdf http://www.ils.uec.ac.jp/~dima/PAPERS/2010superfar.pdf with transformation at the bottom of that table at $P(z)=z - \frac{1+\sqrt{5}}{2}$ I suspect, with that short table we have covered the most of simple elementary superfunctions... « 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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