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

[JmsNxn]

Well I wouldn't be analyzing the Taylor series per se. I'd just like to see a graph of \( f(t) = a\,\{t\}\,b \) for any appropriate constants a and b over \( t\, \epsilon\, [-1, 2] \). My understanding is that the differences between each version of tetration are minute and probably wouldn't affect an approximate graph (It should at least be enough to verify that there are no humps).

I'll give you an email then.