regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational)

[sheldonison]

Thanks sheldon that was really helpful. Is there any code yet generating these two functions?

And my second question still stands, though;
why exactly does \( \text{Usexp}_{\sqrt{2}}(0) = 5.767053... \), is this point arbitrary? If it was shifted to 8 it wouldn't affect its status as a super function of root 2 would it? It's just a horizontal shift right?

Horizontal shift -- yes and no. It is what comes out of the limit equation, that generates Usexp(0), limit as n->infinity. I'll need to dig that equation out. But even if you do a horizontal shift, it gets cancelled out since Uslog is the inverse of Usexp. I do have the lower level primitives, "superf(z)" and a "isuperf(z)" functions in kneser.gp. Type init(sqrt(2)), and those two functions are available. For bases<eta, which also have a lower superfunction, I have also implemented superf2(z), and isuperf2(z).
- Sheldon