Constructing real tetration solutions Daniel Fellow Posts: 247 Threads: 79 Joined: Aug 2007 12/22/2019, 10:53 AM Has anyone considered using the countable complex fixed points to construct real tetrational solutions? Daniel bo198214 Administrator Posts: 1,616 Threads: 102 Joined: Aug 2007 12/22/2019, 10:28 PM Yes, Daniel that's the Kneser-Solution and many of the other methods discussed here are real-analytic solutions based on the primary complex fixed points. Daniel Fellow Posts: 247 Threads: 79 Joined: Aug 2007 12/23/2019, 02:52 AM (12/22/2019, 10:28 PM)bo198214 Wrote: Yes, Daniel that's the Kneser-Solution and many of the other methods discussed here are real-analytic solutions based on the primary complex fixed points. Yes, I'm now familiar with Kneser's approach thanks to your exposition of his work. I was thinking in terms of a countable number of fixed points, but given Kneser's work my requirement might be overkill.   Daniel Daniel bo198214 Administrator Posts: 1,616 Threads: 102 Joined: Aug 2007 12/23/2019, 03:56 PM As far as I know nobody managed to use any other fixpoint-pair than the primary one. To use all the fixpoints seems to be a much stronger demand. sheldonison Long Time Fellow Posts: 684 Threads: 24 Joined: Oct 2008 12/24/2019, 12:10 AM (12/23/2019, 03:56 PM)bo198214 Wrote: As far as I know nobody managed to use any other fixpoint-pair than the primary one. To use all the fixpoints seems to be a much stronger demand. Daniel, Jay, Please see this thread  https://math.eretrandre.org/tetrationfor...hp?tid=452 About a year and half later, post#18, I generated a tetration solution from the secondary fixed point with the caveat that the derivative at the real axis goes to zero; see post#18; #19 in the thread I just linked to.   That solution has f' and f'' and tet(-1)=0; one can imagine that perhaps with the next fixed point pair, perhaps tet',tet'',tet''',tet'''' would all need to be zero ....  I haven't revisited this post since 2011. - Sheldon « Next Oldest | Next Newest »

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