Funny pictures of sexps

[bo198214]

Bo, just to refresh my memory, how are you calculating the isexp_e?

I compute the powerseries of Andrew's slog at x=1. Then I invert this series.
To be more exact:
I consider the Carleman matrix C of the powerseries development of e^(x+1)-1.
Then I compute what Andrew calls Abel matrix.
I.e. the transpose of the suitably truncated C - I. And solve the equation A p = (1,0,0...)
-1+p(x) is then the islog of e^(x+1)-1 at 0.
And p(x-1) is the islog of e^x at 1.
And p^{-1}(x)+1 is the isexp of e^x at 1.

The development of the slog at 1 instead of the normal 0, which implies sexp developed at 0 instead of the normal -1, should allow a convergence radius of 2 instead of 1 for the sexp. But it seems as if the convergence radius is only 1.4, i.e. roughly the imaginary part of the fixed point.

edit: On the other hand probably the at 1 developed slog is different from the at 0 development slog.