[Regular tetration] [Iteration series] norming fixpoint-dependencies

[Gottfried]

i.e. z<> z^z => z^z =/= (z + z^^2)/2.

I explained in an earlier post my misuse of the z^^h-notation. (Oh, that was in the other thread only?, Then - sorry)
Ok. To make ascii-writing short I use it there (and now here) in that meaning:

using a base b, z^^h is b^b^...^b^z where h is the number of b,

in case of continuous: z^^h = \( \exp_b^{oh}(z) \)

I think that "misuse" can be justified since we usually talk about a fixed chosen base ("b") and discuss the change of parameter z as iteration start, h as iteration "height" and z^^h as iteration result. Reading some "z^z" above I think there is a misunderstanding there.

Gottfried