Kneser's Super Logarithm

[sheldonison]

So then it would seem to agree with the Kouznetsov function, then, wouldn't it, i.e. the \( \operatorname{tet}_e(z) \) function developed this way decays to approximately \( 0.318 \pm 1.337i \) as \( z \rightarrow \pm i \infty \)? Hmm. Does this Kneser method work for other bases, too?

Yes, and Yes. I don't think anyone's tried it though.

Can it be used at a complex base, e.g. \( 2 + 1.5i \)?

You could always generate the inverse Abel function from the fixed point for the complex base. But if f(z) is real valued, f(z+1) would have a complex value, so the Kneser mapping couldn't convert the Abel function into a real valued tetration. But it seems like it could generate an analytic complex base tetration where sexp(-1)=0, sexp(0)=1, sexp(1)=2+1.5i, sexp(2)=(2+1.5i)^(2+1.5i) and sexp(-2,-3,-4...)=singularity....