Uniqueness of half-iterate of exp(x) ?

[Gottfried]

which, by definition, can also be written as
\( f(x)=x^2/W(x^2) \)

Hmm, I get the following using Pari/GP:

Code:

x0=1.0
%1876 = 1.00000000000

x1=exp(x0)
%1877 = 2.71828182846

x05 = x0^2/LW(x0^2)
%1878 = 1.76322283435

x05^2/LW(x05^2)
%1879 = 2.91030427217

Perhaps some cofactor could improve the formula?

Gottfried