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 tetration from alternative fixed point sheldonison Long Time Fellow Posts: 683 Threads: 24 Joined: Oct 2008 05/24/2010, 04:41 AM (This post was last modified: 05/24/2010, 04:43 AM by sheldonison.) (05/23/2010, 07:54 AM)bo198214 Wrote: The problem with alternative fixed points is that we dont have a sickel between them. I.e. if we connect two conjugated non-primary fixed points with a straight line, then the image under $e^z$ of this straight line overlaps itself. This is due to the imaginary part of the fixed point pair is apart more then $2\pi$ which makes the image of any connecting line between these fixed points, revolve around 0 at least once.Would this refer to the graph of the complex super-function, generated from the secondary fixed point, or to the graph of the real valued super-exponential, after the Kneser solution? Quote:For Kneser's solution we need a region that is bounded by a line connecting the two fixed points and the image of this line. Perhaps one (you?) could prove, that regardless how you connect a conjugated fixed point pair, that is not the primary one, the image of this line intersects itself or the connecting line; i.e. both lines never delimit a singly connected region. I'd like to graph the 3*pi*i contour line of the super-function generated from the secondary fixed point, 2.0622777296+i*7.5886311785 The super-function "grows" away from the fixed point, and the first n*pi*i contour encountered is the 3*pi*i contour. This is analogous to the primary fixed point, which eventually reaches the pi*i contour. The theory is that the contour line would have real values from -infinity to +infinity, and that the exponent of that contour line, would trace out the real values from -infinity to zero, and the next exponent would trace out the real values from zero to one etc. It is straightforward to generate the super-function from the secondary fixed point, but the inverse super-function is giving me difficulties, and I need to get the iteration equations for the inverse super-function working before I can graph the 3*pi*i contour, and then perhaps I will understand why this contour line does not allow for Knesser's construction. « Next Oldest | Next Newest »

 Messages In This Thread tetration from alternative fixed point - by sheldonison - 05/23/2010, 12:05 AM RE: tetration from alternative fixed point - by bo198214 - 05/23/2010, 07:54 AM RE: tetration from alternative fixed point - by sheldonison - 05/24/2010, 04:41 AM RE: tetration from alternative fixed point - by bo198214 - 05/24/2010, 11:43 AM RE: tetration from alternative fixed point - by sheldonison - 05/24/2010, 03:03 PM RE: tetration from alternative fixed point - by sheldonison - 06/03/2010, 04:13 AM RE: tetration from alternative fixed point - by sheldonison - 06/21/2010, 04:24 PM RE: tetration from alternative fixed point - by bo198214 - 06/27/2010, 06:02 AM RE: tetration from alternative fixed point - by tommy1729 - 06/27/2010, 10:18 PM RE: tetration from alternative fixed point - by bo198214 - 06/28/2010, 03:08 AM RE: tetration from alternative fixed point - by sheldonison - 06/28/2010, 11:03 PM RE: tetration from alternative fixed point - by bo198214 - 06/29/2010, 06:53 AM RE: tetration from alternative fixed point - by sheldonison - 07/01/2010, 03:31 PM RE: tetration from alternative fixed point - by bo198214 - 07/02/2010, 07:37 AM RE: tetration from alternative fixed point - by bo198214 - 07/21/2010, 03:24 AM RE: tetration from alternative fixed point - by sheldonison - 07/21/2010, 04:58 PM RE: tetration from alternative fixed point - by sheldonison - 08/13/2010, 03:53 PM RE: tetration from alternative fixed point - by JmsNxn - 12/05/2011, 07:58 PM RE: tetration from alternative fixed point - by sheldonison - 12/06/2011, 02:43 PM RE: tetration from alternative fixed point - by Daniel - 12/24/2019, 06:26 AM

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