sexp for base (1/e)^e ~= 0.0660?

[sheldonison]

However, I don't think the upper-plane will be periodic, since it appears that applying \( b^z \) repeatedly to \( z \) close to \( \frac{1}{e} \) seems to lead to a slow and oscillatory attraction toward \( \frac{1}{e} \). I suspect \( \lim_{t \rightarrow \infty} \mathrm{tet}_{\left(\frac{1}{e}\right)^{e}}(t + i\delta) = \frac{1}{e} \) for all \( \delta \ge 0 \).

I'm not looking for an exact 2-periodic solution; but the solution I'm looking for has limiting behavior that looks more and more like a periodic function as imag(z) goes to infinity. I have the example for base=1.96514 + 0.441243i, which is an indifferent with pseudo period=5, whose sexp(z) solution as imag(z) increases to infinity looks increasingly like \( \exp(2\pi i z/5) \). Anything else I would post now would be gibberish, because I haven't gotten a form for the solution yet, even though I can almost see it
- Sheldon