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 Transseries, nest-series, and other exotic series representations for tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 12/15/2009, 01:00 PM (This post was last modified: 12/15/2009, 01:13 PM by bo198214.) (12/15/2009, 12:46 PM)bo198214 Wrote: Hm, I have to look where the error is then. It appears that the Faulhaber sum is not monotonic (which I assumed), i.e. we dont have that from $f(x) follows that $\sum_{x} f(x) < \sum_{x} g(x)$. This puzzles me a bit, shouldnt one expect that from a sum operator? But no, one shouldnt. The simplest example is perhaps $f(x)=1$ and $g(x)=1+x^2$ with the Faulhaber sums $x$ and $\frac{1}{3} x^{3} - \frac{1}{2} x^{2} + \frac{7}{6} x$; the latter cuts $x$ at 0 because the first derivative there is different from 1. « 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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