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 Iterating at fixed points of b^x bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 09/12/2007, 10:00 PM (This post was last modified: 09/12/2007, 10:01 PM by bo198214.) Daniel Wrote:bo198214 Wrote:Daniel Wrote:Just consider the term $\ln(a)^n$ in $\;^{n}b = a + \ln(a)^n \; (1-a) + \ldots$.Öhm, a bit more explanative?This is just a version of my definition for extending tetration from http://tetration.org/tetration_net/tetra...omplex.htm . The Taylor series of $\;^{n}b$ taken at $a$ has the zero term at the fixed point of course and then $D f^n(a)= f'(a)^n = \ln(a)^n$. This is surely true, but I dont see the connection to showing that the regular iteration at fixed point $a$ is non-real for real arguments $x$. Natural numbered iterations of $b^x$ at any fixed point of course yield real values for real arguments $x$, just $\exp_b^{\circ n}(x)$. Which is no more true for fractional iterations. « Next Oldest | Next Newest »

 Messages In This Thread Iterating at fixed points of b^x - by bo198214 - 09/08/2007, 10:02 AM The fixed points of e^x - by bo198214 - 09/08/2007, 10:34 AM The fixed points of b^x - by bo198214 - 09/08/2007, 11:36 AM RE: Iterating at fixed points of b^x - by jaydfox - 09/12/2007, 06:23 AM RE: Iterating at fixed points of b^x - by bo198214 - 09/12/2007, 09:54 AM RE: Iterating at fixed points of b^x - by GFR - 10/03/2007, 11:03 PM RE: Iterating at fixed points of b^x - by Gottfried - 10/04/2007, 06:53 AM RE: Iterating at fixed points of b^x - by bo198214 - 10/04/2007, 01:30 PM RE: Iterating at fixed points of b^x - by bo198214 - 10/04/2007, 05:54 PM RE: Iterating at fixed points of b^x - by Gottfried - 10/04/2007, 11:05 PM RE: Iterating at fixed points of b^x - by GFR - 01/31/2008, 03:07 PM

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