Computing Abel function at a given center

[Gottfried]

I finally got back to this, and it appears that shifting the center prior to solving the system produces the same results as shifting the center after solving the system. This means we're limited by the radius of convergence at the origin, which is to say, the system explicitly solves at the origin, not where we recenter it.

Hmm, I never understood this "shifting", maybe I'm compeltely wrong with the following.
In my matrix-method it occured, that I can use a triangular operator (with some advantages for numericla computation) if I rewrite

V(x)~ * Bs = V(s^x) ~

into

V(x/t - 1)~ * Qs = V(s^x/t - 1)~
or
V(x - t)~ * Rs = V(s^x-t)~

where t is the fixpoint of s, and Qs or Rs are triangular.

I don't have then general powers easily(but possibly manageable), but I have better access, for instance to the inverse of the function or for more general s.

Is this equivalent to this "shifting"?

Gottfried