(09/12/2009, 07:40 AM)mike3 Wrote: Because it's a repelling point, so the resulting superfunction will still be entire, and I want to try and find one with the singularities, etc., as that is more like what is expected from "tetration".
The method does anyway not work, even if we take the regular iteration at one of the attracting fixed points. Because the regular iteration returns a strictly increasing function, particularly \( g^{\circ 1/2} \) is strictly increasing and hence \( g^{\circ 1/2} \neq f \) because \( f \) is strictly decreasing.
Its a bit like you want to know what \( (-3)^t \) is. Then you can not just consider \( ((-3)^2)^{t/2}=3^t \) as \( 3^t\neq (-3)^t \).
PS: Quoting policy is to only quote what is necessary for your reply.
