01/14/2016, 05:05 AM
(This post was last modified: 01/14/2016, 05:33 AM by sheldonison.)
(01/14/2016, 12:59 AM)andydude Wrote: Why is this called "Kneser"? can you provide the article or reference that inspired this algorithm?
Take a look at these two posts; Henryk's post, http://math.eretrandre.org/tetrationforu...hp?tid=213
and Jay's post, http://math.eretrandre.org/tetrationforu...hp?tid=358
Kneser's Riemann mapping results in \( \exp(2\pi i \cdot f(z)) \) where \(
f(z)=z+\theta(z)=\alpha(\text{sexp}(z))\;\; \) which has been wrapped around a unit circle by using the substitution \( z = \frac{\log(y)}{2\pi i} \). So my approach is related, and mathematically equivalent, but not identical. In the approach used in my kneser.gp program, I iterate, generating increasingly accurate \( \theta(z) \) approximations from increasingly accurate sexp(z) taylor series approximations where in the limit, \( \text{sexp}(z)=\alpha^{-1}(z+\theta(z)) \)
- Sheldon