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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, 03:16 PM (This post was last modified: 12/14/2009, 03:21 PM by bo198214.) Mike, I have another bad news, I found out that not even the Faulhaber sum of $e^{\frac{x^2}{2}}$ is convergent, contrary to what I said before because it looks convergent up to n=100 terms; so your transseries sum $e^{e^x}$ can not be convergent. The first coefficient of the Faulhaber sum for $n$ terms: Code:n= 100 : 1.1 n= 101 : 1.0 n= 102 : 1.0 n= 103 : 1.2 n= 104 : 1.2 n= 105 : 0.68 n= 106 : 0.68 n= 107 : 2.2 n= 108 : 2.2 n= 109 : -1.8 n= 110 : -1.8 n= 111 : 9.2 n= 112 : 9.2 n= 113 : -22. n= 114 : -22. n= 115 : 67. n= 116 : 67. n= 117 : -190. n= 118 : -190. n= 119 : 570. « 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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