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 Transseries, nest-series, and other exotic series representations for tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 12/14/2009, 02:19 PM (12/14/2009, 02:11 PM)kobi_78 Wrote: I have been exploring the sum operator, what you guys call "continuum sum" for a couple of years as a hobby. I think I have an idea how to sum $e^{x^2}$. Recall that $e^{x^2} = \lim_{n \to \infty} \left( 1 + \frac{x^2}{n} \right)^n$ Now calculate the polynomial sum of $\left( 1 + \frac{x^2}{n} \right)^n$ (using Faulhaber's formula). This seems to convergent to a nice function. Wow, what a debut! Hey Kobi, welcome to the forum! Did you also find out something about the uniqueness of the obtained functions? Are there perhaps examples where you group the terms in a different way and get different results? « 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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