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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#22

12/15/2009, 01:17 AM (This post was last modified: 12/15/2009, 01:17 AM by bo198214.)

(12/14/2009, 09:22 PM)mike3 Wrote: How does that refute the summation I gave with the transseries? That involves continuum-summing on terms of the form $ae^{nx}$ , not $ae^{nx^2}$ or $ae^{x^n}$ or something like that.

Its because $\frac{x^2}{2}<e^x$ .
Thatswhy both Faulhaber sums are also in the < relation.
Thatswhy the sum of $e^{\frac{x^2}{2}}$ and of $e^{e^x}$ are also in this relation.

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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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