Does anyone have taylor series approximations for tetration and slog base e^(1/e)?

[bo198214]

I'll describe what I did to generate the Taylor series for sexp(z). Its not fancy or anything -- its just what worked for me to investigate base eta, with its parabolic convergence. I use pari-gp, to generate an interpolating polynomial. Only I center the polynomial around sexp(100), where the sexp(z) function is already converging towards e, and is fairly well behaved. Then I generate 25 points on either side of sexp(100), using 67 digits of precision.

You mean, you take the interpolation polynomial at the integer-points of sexp?
Yeah true, that also yields regular iteration.
I think we discussed this a lot with Ansus - the Newton (interpolation) formula.