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 Generalized recursive operators GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 03/11/2008, 04:40 PM (This post was last modified: 03/12/2008, 12:47 AM by GFR.) Ivars Wrote:So what are the exact values for : $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) = ?$ $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 9\\\hline\end{tabular} b) = ?$ $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 11\\\hline\end{tabular} b) = ?$ etc?Well, always for $b < 0$ let us start from (Hey, boys, I am starting using TeX ... Waaaoow!): $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) = c$ For an estimation of $c$, I think we may proceed like this, assuming the new more precise asymptotic value obtained by Andydude (step 0): $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -1.85..$, and: $\lim_{b\rightarrow-1.85..}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -\infty$ Then: step 1 - Calculate $y = e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b$ vor various values of $b < 0$ and produce a graphical continuous and smooth plot, if possible; step 2 - Produce the graphical inversion of the previous plot, always in the $b < 0$ domain, so obtaining the pentalog of $b < 0$ ; step 3 - Estimate the intersection between the two pentation/pentalog diagrams (always in $b < 0$), which should coincide with one the pentation fixpoints for $y = b$. The coordinate of this point should be what we may call $h$. This $h$ is the coordinate of the penta-fixpoint and, therefore of the hexation asymptote. We can see thay it must be $h < -1.85..$. step - Proceed again as in step 3 with the hexation/hexalog plots and the result will be $c < h$, such that: $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) = c$, and: $\lim_{b\rightarrow c}(e \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) = -\infty$ And ... so on !!!! However, ... it is a very long way ... Perghaps there are shortcuts. GFR [Sorry, Administrator, these comments of mine, apart the first 5 lines are completely wrong. I shall correct them asap. Perhaps, I was tired! - GFR] « Next Oldest | Next Newest »

 Messages In This Thread Generalized recursive operators - by Whiteknox - 11/23/2007, 06:42 AM RE: Generalized recursive operators - by bo198214 - 11/23/2007, 08:41 AM RE: Generalized recursive operators - by Whiteknox - 11/23/2007, 03:57 PM RE: Generalized recursive operators - by andydude - 11/25/2007, 01:02 AM RE: Generalized recursive operators - by andydude - 11/29/2007, 04:45 AM RE: Generalized recursive operators - by andydude - 11/29/2007, 05:55 AM RE: Generalized recursive operators - by andydude - 11/29/2007, 06:20 AM RE: Generalized recursive operators - by Gottfried - 11/29/2007, 08:14 AM RE: Generalized recursive operators - by andydude - 11/30/2007, 06:12 PM RE: Generalized recursive operators - by andydude - 11/30/2007, 09:18 PM RE: Generalized recursive operators - by bo198214 - 03/07/2008, 06:58 PM RE: Generalized recursive operators - by Ivars - 02/02/2008, 10:11 PM RE: Generalized recursive operators - by Whiteknox - 12/01/2007, 04:59 AM RE: Generalized recursive operators - by Ivars - 02/03/2008, 10:41 AM RE: Generalized recursive operators - by andydude - 02/11/2008, 09:47 PM RE: Generalized recursive operators - by Ivars - 02/14/2008, 06:05 PM RE: Generalized recursive operators - by GFR - 02/03/2008, 04:12 PM RE: Generalized recursive operators - by Ivars - 02/03/2008, 08:48 PM RE: Generalized recursive operators - by GFR - 02/06/2008, 02:44 PM RE: Generalized recursive operators - by Ivars - 02/06/2008, 02:56 PM RE: Generalized recursive operators - by Ivars - 02/06/2008, 03:43 PM RE: Generalized recursive operators - by GFR - 03/10/2008, 09:53 PM RE: Generalized recursive operators - by GFR - 03/11/2008, 10:24 AM RE: Generalized recursive operators - by bo198214 - 03/11/2008, 10:53 AM RE: Generalized recursive operators - by GFR - 03/12/2008, 12:13 AM RE: Generalized recursive operators - by GFR - 03/13/2008, 06:41 PM RE: Generalized recursive operators - by Stan - 04/04/2011, 11:52 PM

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