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 Transseries, nest-series, and other exotic series representations for tetration bo198214 Administrator Posts: 1,395 Threads: 91 Joined: Aug 2007 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. « Next Oldest | Next Newest »

 Messages In This Thread Transseries, nest-series, and other exotic series representations for tetration - by mike3 - 11/26/2009, 09:46 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by Daniel - 11/26/2009, 03:57 PM RE: Transseries, nest-series, and other exotic series representations for tetration - by bo198214 - 11/26/2009, 04:42 PM RE: Transseries, nest-series, and other exotic series representations for tetration - by Daniel - 11/29/2009, 09:09 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by bo198214 - 11/29/2009, 09:38 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by Daniel - 12/01/2009, 02:56 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by bo198214 - 12/01/2009, 09:08 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by tommy1729 - 12/01/2009, 10:22 PM RE: Transseries, nest-series, and other exotic series representations for tetration - by mike3 - 11/27/2009, 01:29 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by andydude - 11/28/2009, 04:56 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by mike3 - 11/28/2009, 06:36 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by mike3 - 11/28/2009, 06:50 AM RE: Transseries, nest-series, and other exotic series representations for tetration - by kobi_78 - 12/14/2009, 07:17 PM

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