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 elementary superfunctions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 04/18/2010, 01:17 PM (This post was last modified: 04/18/2010, 01:19 PM by bo198214.) Did we mention already the tangent? It has this nice addition theorem: $\tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)}$ which brings us the superfunction: $\sigma(z)=\tan(z\cdot\arctan( c))$ $\sigma(z+1)=\frac{\sigma(z)+c}{1-c\sigma(z)}=f(\sigma(z))$ for the function $f(z)=\frac{z+c}{1-cz}$ $f$ is another particular case of a linear fraction (where the regular iteration at both fixed points coincide). The two (non-real) fixed points are: $\frac{z+c}{1-cz}=z$, $z+c=z-cz^2$ $z=\pm i$ for $c\neq 0$ « 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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