x↑↑x = -1

[sheldonison]

....
ah so you do claim the 2 theta function agree on the real line.

But then how can they be different ??
By schwarz reflection and analytic continuation it seems weird that 2 analytic functions can agree on the real line , yet be different off the real line...

For a complex base, tet is not a real valued function at the real axis. But if the base is real, then yes, the two theta functions agree naturally due to Schwarz reflection involving L and L*. So the complex tet function naturally becomes the Kneser solution for a real valued base, which is exactly what we need. I'm not trying to address how to compute the two theta functions; that is a much difficult post to write, but I do get very good convergence for many complex bases. The key is to iterate all three Taylor series functions, plus a lot of magic coding. And magically, all three functions converge into excellent numeric agreement for the unit circle Taylor series, where each representation is used where it can give accurate results.