01/07/2020, 03:55 PM

01/16/2020, 10:08 PM

(01/07/2020, 03:55 PM)Daniel Wrote: [ -> ]Check out Moving between Abel's and Schroeder's Functional Equations

Hey Daniel,

what if

Then Schroeder's equation , but is complex.

Personally I think I prefer instead of for the complex valued Abel function.

There is a pair of complex valued Abel functions for the two complex conjugate fixed points, and there is a singularity at

Anyway, Kneser's tetration uses a Riemann mapping of , wrapping the real axis around a unit circle to eventually get to

where there are two 1-cyclic theta(z) functions

where k is a constant as Im(z) gets arbitrarily large, and Kneser's slog or the inverse of Tetration would be

tau^{-1}(z) is also a z+1-cyclic function used to generate Tet(z) from the inverse of the complex valued Abel function.

https://math.eretrandre.org/tetrationfor...hp?tid=213

https://math.stackexchange.com/questions...55#2308955