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 The fermat superfunction tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 08/13/2013, 12:23 PM (This post was last modified: 08/13/2013, 12:27 PM by tommy1729.) Let f(x) = (x-1)^2 + 1. If we want the half-iterate of f(x) for x>1 we can use S(S^[-1](x)+1/2) where S is the superfunction of f(x). For x>2 this superfunction is F(x) = 2^(2^x) + 1. Hence I call that the fermat superfunction. This fermat superfunction F(x) is entire so there are no other branches. F^[-1] does have branches though but they are easy to understand. Notice F(x) = 1 has no complex solution. ( 1 is the other fixpoint of f(x) ) But what do we do for the other nonparabolic fixpoint of f(x) ? What superfunction belongs there ? Is this related to branches of F^[-1] ? regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread The fermat superfunction - by tommy1729 - 08/13/2013, 12:23 PM RE: The fermat superfunction - by tommy1729 - 03/23/2014, 12:15 AM RE: The fermat superfunction - by mike3 - 03/23/2014, 11:29 PM RE: The fermat superfunction - by tommy1729 - 03/24/2014, 12:58 AM

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