Equations for Kneser sexp algorithm

[sheldonison]

Ahhh! Now I understand

\( \lim_{z\to i\infty} e^{2n\pi i z} = 0 \)


you choose *the* \( \theta \) that that decays towards ioo.
Is this a uniqueness criterion for \( \theta \)?
I mean that \( \text{superf}(z+\theta(z)) \) is a real analytic superfunction and \( \theta \) decays towards \( i\infty \).
Could be, ha?

Its definitely a uniqueness criterion. Another way to think about it is from the point of view that \( \theta(z) \) is connected to Kneser's unique Riemann mapping, since \( \rho^{-1}(z)=\theta(z)+z \). But yes, any sexp(z) solution would either be the unique solution, with \( \theta(z) \) exponentially decaying to a constant as \( z\to+i\infty \), or else if it is any other solution, than \( \theta(z) \) grows exponentially as \( z\to+i\infty \).
- Sheldon