eta as branchpoint of tetrational

[sheldonison]

@sheldonison: Thanks for the coeffs. I'd like to see if I could make a color graph. What is the starting point you use for the upper regular superfunction? (i.e. the value at 0)

Hey Mike,
\( \text{Usexp}_{\sqrt{2}}(z) \) is developed from the L=4 fixed repelling point, with \( \text{Usexp}_{\sqrt{2}}(0)=5.767053253764297762019157833944 \).
\( \text{Lsexp}_{\sqrt{2}}(z) \) is developed from the L=2 fixed attracting point, with f(-1)=0, f(0)=1, f(1)=sqrt(2), and the "merger" of the two functions takes place at half the period of the LSexp=8.57i. In practice, one could literally say that for imag(z)<=8.57i Fatou(z)=Lsexp(z), and for imag(z)>=8.57i Fatou(z)=Usexp(z+k), ignoring any of the theta(z) terms, because the two functions are so very nearly identical where they merge.
- Sheldon