Transseries, nest-series, and other exotic series representations for tetration

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Transseries, nest-series, and other exotic series representations for tetration

bo198214 Offline

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#17

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?

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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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