andydude Wrote:See Analytic solution of F(z+1)=exp(F(z)) in complex z-plane for more information.

About the uniqueness: It is well known that if we have a solution of the Abel equation then for any 1-periodic function also is a solution to the Abel equation. (Because ).

So let be one solution of

(*) with

(**) and

then is another solution of (*). Let us now consider (**). We know that and

. As

at least for x=0 also

[edit] fixed some negligences. [/edit]