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 Continuous iteration from fixed points of base e jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 11/22/2007, 09:08 PM Interestingly, the singularity is repeated at every tetrate of e (0, 1, e, e^e, etc.), and the other singularities are scaled copies of the one at the origin, plus the constant n for the n-th tetrate. The scaling factor is simple to calculate. The singularity at the n-th tetrate is ${}^{n} e$ times bigger than the scaling factor at the (n-1)-th tetrate. This can be seen by considering: $ \begin{eqnarray} {\Large e}^{\left({}^{n-1}e+\delta\right)} & = & {\Large e}^{\left({}^{n-1}e\right)} {\Large e}^{\delta} \\ & = & {}^{n}e \left(1+\delta+\mathcal{O}(\delta^2)\right) \\ & = & {}^{n}e + {}^{n}e \delta \end{eqnarray}$ ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread Continuous iteration from fixed points of base e - by jaydfox - 09/20/2007, 05:46 AM RE: Continuous iteration from fixed points of base e - by Gottfried - 09/20/2007, 06:56 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/24/2007, 05:37 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/24/2007, 05:53 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/24/2007, 06:37 AM RE: Continuous iteration from fixed points of base e - by andydude - 09/24/2007, 05:26 PM RE: Continuous iteration from fixed points of base e - by andydude - 09/24/2007, 05:42 PM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/24/2007, 06:01 PM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/24/2007, 06:16 PM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/27/2007, 07:00 AM RE: Continuous iteration from fixed points of base e - by bo198214 - 10/07/2007, 08:18 PM RE: Continuous iteration from fixed points of base e - by bo198214 - 10/08/2007, 08:28 PM RE: Continuous iteration from fixed points of base e - by bo198214 - 10/08/2007, 09:05 PM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/28/2007, 09:21 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 09/28/2007, 09:34 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 10/13/2007, 07:13 AM RE: Continuous iteration from fixed points of base e - by GFR - 10/13/2007, 10:05 AM RE: Continuous iteration from fixed points of base e - by andydude - 10/16/2007, 06:21 PM RE: Continuous iteration from fixed points of base e - by jaydfox - 10/16/2007, 09:07 PM RE: Continuous iteration from fixed points of base e - by andydude - 10/20/2007, 05:15 PM RE: Continuous iteration from fixed points of base e - by jaydfox - 11/22/2007, 04:50 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 11/22/2007, 06:10 AM RE: Continuous iteration from fixed points of base e - by jaydfox - 11/22/2007, 09:08 PM

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