periodic ...

[sheldonison]

i had some ideas relating tetration and superfunctions in general to the following properties :

A) f(z) is Coo and Im f(z) is periodic.

B) f(z) is Coo and Re f(z) is periodic.

C) A) and B) but f(z) is not periodic.

what is known about functions satisfying A) B) or C) ?

anything special about them ?

are there series expansions only valid for such functions ?

I think the Taylor series expansions are usually generated by a matrix. When the superfunction is generated from the fixed point of L for that base, then you have a limit equation, which can indirectly be used to generate a Taylor series. Henryk posted something the other day, that might be relevant (true or false logarithm). But in general, I don't think much is known about generating the Taylor series terms in a closed form.

I don't know any cases where Re f(z) is periodic. Im f(z) is periodic for bases<eta.
- Sheldon