09/18/2009, 01:00 PM
(09/18/2009, 12:16 PM)tommy1729 Wrote: i mean , you get a fixed point for b^x = x , so you just use that fixed point to do regular half-iterates ?
As I already wrote there are formulas for regular iteration for \( |\lambda|\neq 0,1 \) and for \( \lambda=1 \) (where \( \lambda \) is the derivative at the fixed point). In the case \( b=e^{-e} \) the derivative is \( \lambda=-1 \), so you have digg deeper in the literature (though the matrix power iteration at that fixed point should do also, however if \( |\lambda|=1 \) usually the resulting powerseries does not converge) about the case where \( \lambda \) is a (in our case: second) root of unity.
For the case \( 0<b<e^{-e} \) we have a repelling fixed point. This gives an entire solution, which would imply that \( \operatorname{sexp}(-1)\neq 0 \). This is not what mike3 wants. There should be a singularity at -2.
Its also slightly unpolite to not read the thread and then ask questions that are already answered/explained in the thread.
