11/20/2012, 11:46 PM
(This post was last modified: 11/20/2012, 11:53 PM by sheldonison.)
(11/20/2012, 11:32 PM)tommy1729 Wrote: I think the same applies to the base change ...Yes! The exact same thing applies to the base change. Iterating \( s(z)=\exp(z-1) \) is exactly analogous to iterating tetration base \( \eta=\exp(1/e) \). Then, taking the logarithm as the first step in the base change results in singularities whenever \( s^{[z]}=2n\pi i \), where \( \log(s^{[z+1]})=\log(e^{2n\pi i}-1)=\log(0) \)
I do not immediately know a way around it.
Actually, for every singularity in the base change, there are two singularities for 2sinh(z), and the singularities for \( 2n\pi i \) for both functions are very nearly in the same place in the complex plane!
- Sheldon