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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, 02:45 PM (This post was last modified: 12/14/2009, 02:48 PM by bo198214.) (12/14/2009, 02:11 PM)kobi_78 Wrote: 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. But wait, first it *seems* to converge, however later it takes off. E.g. if I compute the coefficient of x, I get rounded to two significant digits (scroll down): Code:n= 60 : 1.2 n= 61 : 1.2 n= 62 : 1.2 n= 63 : 1.1 n= 64 : 1.2 n= 65 : 1.1 n= 66 : 1.2 n= 67 : 0.96 n= 68 : 1.7 n= 69 : -0.14 n= 70 : 4.5 n= 71 : -7.8 n= 72 : 25. n= 73 : -64. n= 74 : 180. n= 75 : -500. n= 76 : 1400. n= 77 : -4100. n= 78 : 12000. n= 79 : -35000. This is not a rounding error as I compute with fractions and do the rounding only for better visibility. « 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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