Re: Tetration again!

Am 19.12.2007 05:55 schrieb mike3:
On Dec 18, 3:13 am, Gottfried Helms <he...@xxxxxxxxxxxxx> wrote:
Am 18.12.2007 08:14 schrieb mike3:

PS. "Tower" here (as opposed to "base") is what you call
"height" -- I'm using the term "Tower" by analogy with
"power" -- (T)etrational p(OWER) -> TOWER, and as a pun.
:-))

Ahh, yes! I got it.


Heh.

Anyway, what about the tetration of an "easy"
base, like the base e that I discussed?

I meant "easy" for bases 1/e^e + eps < base < e^(1/e)-eps
where the powerseries converge for each height/infinite
height = according power of tetration-matrix


I noticed something too. The "linear" tetration
given seems to be continuously differentiable
when the base is e. This makes sense, since it
says that at each integer the derivative multiples
by the natural log of the base, and the natural
log of e is 1, so no change -- it's continuous.
Is that something interesting?

Maybe... Someone else may consider this... sorry, no
idea currently.

Gottfried
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Gottfried Helms, Kassel
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