Posts: 1,370

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Joined: Feb 2009

could it be true that by andrew robbins method :

f(x) = 2^f(x-1) f(0) = 1 ( coo base 2 tetration thus )

g(x) = df^2/dx^2 f(x)

g(0) = 0 ???

regards

tommy1729

Posts: 509

Threads: 44

Joined: Aug 2007

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nth apprimation to intuitive tetration (base 2):

Code:

`n sexp_2'(0) = -slog_2''(1)/slog_2'(1)^3`

===============

5 0.0108519

10 0.0171036

15 0.0173285

20 0.0173507

25 0.0173537

30 0.0173539

So it seems as though this sequence converges to something other than zero.

If you're looking for a base with "nice" properties, I would recommend base (3.0885325).

What makes base (3.0885325) special is that it is the maximizer of

, and maximum of

over the interval (?, 1.6353245). I think this is analogous to how base (e) is the maximizer of

and the maximum of

over the interval (0.065988, 1.44467).