11/26/2009, 04:42 PM
(11/26/2009, 03:57 PM)Daniel Wrote: The most general method I've developed for extending tetration is based on using a system of nested summations like you are talking about.
So you can compute a converging nested series for a fractional iterate of \( e^x-1 \)? This would be very interesting as it was shown by Baker and Écalle that the (ordinary) power series of the regular iterates of \( e^x-1 \) do not converge (except for integer iterates of course). I think though there is a paper of Écalle where he shows that they are Borel-summable despite. Unfortunately its difficult (by a lack of theorems/propositions) to see on your site what you are actually able to do with your sums.
@Mike3: Yes really interesting stuff those transseries, but in the moment out of my scope to dive deeper into the topic to be able to apply it to continuum sums.
