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 Andrew Robbins' Tetration Extension andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/13/2007, 05:45 PM Indeed, that would be strange. I'm not assuming convergence, but I am assuming that: convergence of the finite series (approximations with coefficient approximations as well) to the infinite series, or in other words: $\lim_{n\rightarrow\infty} \text{slog}_b(z)_n$ where $\text{slog}_b(z)_n = \sum_{k=0}^{n}s_{nk}z^k$ or in other words: $\lim_{n\rightarrow\infty}\sum_{k=0}^{n} s_{n k}z^k$, and convergence of the infinite series (whose coefficients must also converge), or in other words: $\lim_{n\rightarrow\infty}\sum_{k=0}^{n} s_{\infty k}z^k$ are equivalent, but this may be an error as well. What I can prove is that for the nth approximation of the super-log (the finite series): As $b \rightarrow 1$, $s_{nk} \rightarrow (-1, 0, 0, \cdots, 0, 0, 1)$ with n+1 entries. As $b \rightarrow \infty$, $s_{nk} \rightarrow (-1)^{k-1} \left({n \atop k}\right)$ with k = 0 .. n. From this it is easy to show $\sum_{k=0}^{n} (-1)^{k-1} \left({n \atop k}\right) z^k = -(1-z)^n$ Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Andrew Robbins' Tetration Extension - by bo198214 - 08/07/2007, 04:38 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/18/2007, 08:20 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/19/2007, 09:50 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/20/2007, 02:22 PM RE: Andrew Robbins' Tetration Extension - by andydude - 11/12/2007, 08:43 AM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 06/26/2009, 10:51 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 06/27/2009, 09:39 AM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 06/28/2009, 12:08 AM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/06/2007, 04:17 AM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/06/2007, 04:27 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/06/2007, 10:57 AM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/06/2007, 01:58 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/06/2007, 03:58 PM RE: Andrew Robbins' Tetration Extension - by jaydfox - 11/12/2007, 09:14 AM RE: Andrew Robbins' Tetration Extension - by andydude - 11/12/2007, 09:56 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/12/2007, 08:05 PM RE: Andrew Robbins' Tetration Extension - by andydude - 11/13/2007, 12:16 AM RE: Andrew Robbins' Tetration Extension - by bo198214 - 11/13/2007, 10:21 AM RE: Andrew Robbins' Tetration Extension - by andydude - 11/13/2007, 05:45 PM RE: Andrew Robbins' Tetration Extension - by Gottfried - 03/17/2008, 07:52 AM RE: Andrew Robbins' Tetration Extension - by Gottfried - 03/17/2008, 06:09 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 06/29/2009, 08:20 PM RE: Andrew Robbins' Tetration Extension - by andydude - 07/27/2009, 08:10 AM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/11/2009, 12:18 PM RE: Andrew Robbins' Tetration Extension - by jaydfox - 08/11/2009, 07:06 PM RE: Andrew Robbins' Tetration Extension - by jaydfox - 08/11/2009, 07:12 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/23/2009, 02:45 PM RE: Andrew Robbins' Tetration Extension - by bo198214 - 08/23/2009, 03:23 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/26/2009, 04:01 PM RE: Andrew Robbins' Tetration Extension - by andydude - 09/04/2009, 06:42 AM RE: Andrew Robbins' Tetration Extension - by Gottfried - 12/28/2009, 05:21 PM RE: Andrew Robbins' Tetration Extension - by tommy1729 - 08/18/2016, 12:29 PM RE: Andrew Robbins' Tetration Extension - by Gottfried - 08/22/2016, 04:19 PM

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