Approaches to Tetration

[Gottfried]

Code:

- Approaches to tetration

  We may classify the approaches to tetration in two classes: a "binary operator
  approach" and an "iterative series approach"

I dont get this classification.
The main goal is to find a[4]x or generally a[n+1]x.
As a tool to do so we use non-integer iteration.
As a tool for non-integer iteration we use series expansions or limit formulas (like for example the formula for the schroeder function \( \sigma(x)=\lim_{n\to\infty} f^{\circ n}(x)/f'(0)^n \)).

And if we are in a good mood we even consider a[q]b for non-integer q.

Hmm - I'm focusing different paradigms here; the goal to extend the operator hierarchy is not always driven by a functional representation. One may call it a "naive" approach - but this sounds somehow pejorative in some ears. Anyway - there is a strong effort to extend the (binary) operator hierarchy solely based on the properties of the usual operators.
I think, we should refer to this as well (it is often the first approach to tetration, btw).