08/15/2007, 09:47 PM
Hm, not sure. It is a strange mixture from several techniques.
1. technique: search for a fixed point and take the unqiue \( t \)-th iterate there. This approach is due to Kneser, however yields complex values for real arguments, because all the fixed points are complex. I dont know whether it even yields the same result for each fixed point of exp.
2. technique: piecewise construction such that all the derivates are continuous at the joining points, this was performed by Andrew Robbins, however on the slog.
So this approach seems to be a mixture from 1. and 2. for sexp.
Makes this sense? I mean it was for good reason that Andrew worked with the slog and not with sexp. And why Gus then needs a fixed point to develop a series?
1. technique: search for a fixed point and take the unqiue \( t \)-th iterate there. This approach is due to Kneser, however yields complex values for real arguments, because all the fixed points are complex. I dont know whether it even yields the same result for each fixed point of exp.
2. technique: piecewise construction such that all the derivates are continuous at the joining points, this was performed by Andrew Robbins, however on the slog.
So this approach seems to be a mixture from 1. and 2. for sexp.
Makes this sense? I mean it was for good reason that Andrew worked with the slog and not with sexp. And why Gus then needs a fixed point to develop a series?