Half-iterate exp(z)-1: hypothese on growth of coefficients

[tommy1729]

oh and ofcourse there is also the following idea :

define g(g(x)) = exp(x) - 1.

solve in the usual way at the parabolic fixpoint ( from julia )

now take the taylor expansion at x = 1 

so we arrive at

g(x) = sum a_n (x-1)^n

where the a_n are from the taylor expansion at 1.

Now expand ( use binomium ) to get 

g(x) = sum a_n (x-1)^n = sum b_n x^n

this might help to prove the bounds.


Not 100 % sure this works though since we are at the edge of convergeance ...

A combination with the integral idea from above might be fruitful.


regards

tommy1729