03/21/2010, 11:03 PM
(03/21/2010, 01:04 PM)bo198214 Wrote:(03/20/2010, 08:12 AM)mike3 Wrote: However, for it to be not real valued in \( (1, e^{1/e}] \) and real valued in \( (e^{1/e}, \infty) \) would imply there is a singularity/branchpoint at \( b = e^{1/e} \), hence not holomorphic there, eh?
ya I would say so, that each non-integer iterate has a singularity as a function in \( b \) at \( e^{1/e} \).
So does this mean the original hypothesis that it "depends holomorphically on \( b \)" (apparently across \( e^{1/e} \) since you contrast this behavior with that of the "usual" regular iteration) was wrong?
