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Transseries, nest-series, and other exotic series representations for tetration
#3
(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 ? This would be very interesting as it was shown by Baker and Écalle that the (ordinary) power series of the regular iterates of 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.
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RE: Transseries, nest-series, and other exotic series representations for tetration - by bo198214 - 11/26/2009, 04:42 PM

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