A nice series for b^^h , base sqrt(2), by diagonalization

[Gottfried]

Don't know yet, whether this has some benefit so far.

It looks, as if we had a discussion of that recently in Upper superexponential

I'm excerpting a bit of Henryk's post:

As it is well-known we have for the regular superexponential at the lower fixed point.

This can be obtained by computing the Schroeder function at the fixed point of .

(...)
Now the upper regular superexponential is the one obtained at the upper fixed point of .
For this function we have however always , so the condition can not be met.
Instead we normalize it by , which gives the formula:
(*1)
(...)

My construction in the previous post was obviously the same as that above construction (*1) ... Gottfried (I added the comments //... )

Then we can write

and the k'th coefficient in my first mail is just 2* C^k * d_k in the formula above.

where the fixpoint "a" is simply given as constant 2 and could be generalized to the symbol. The sum-expression describes the inverse of the schröder-function chi^-1 in Henryk's post. The formula for the repelling fixpoint replaces simply 2 by 4 and (1/2-1) by (5/4-1) and uses the adapted schröder-function. So I think it's useful to redirect replies to the other thread...