Approaches to Tetration

[bo198214]

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- 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.