x↑↑x = -1

[tommy1729]

....
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.

Im aware of that.

I mean mapping a continu line on the complex plane to the positive reals.

For instance mapping f(4+3i) to g(1) as a point example.

... it seems weird that 2 analytic functions can agree on the real line , yet be different off the real line...

so f(1) = g(1) = a , f(2) = g(2) = b , ... for all positive reals ... yet f and g are different ??

regards

tommy1729