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 regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 sheldonison Long Time Fellow Posts: 668 Threads: 24 Joined: Oct 2008 06/25/2013, 01:37 PM (This post was last modified: 06/25/2013, 01:50 PM by sheldonison.) (06/25/2013, 10:45 AM)Gottfried Wrote: (06/24/2013, 04:09 PM)sheldonison Wrote: What is the definition/equation for a Kneser solution dual? The Kneser solution is not periodic. Would the dual of -infinity, which is sexp(-2) be sexp(2)? - Sheldon.... if $K(h,x)$ would denote the Kneser-method iteration from x using height h, then in our case with base = sqrt(2)... GottfriedThe Kneser complex conjugate solution is only defined for bases>e^(1/e), not for base=sqrt(2), where we normally use regular iteration instead. The Kneser solution is built on a modification of the complex Schroder function solution, but for the Kneser solution, S(0) is always singularity, so there would be no definition for a dual of 0. For the tangent angle sum equation, the Schröder function of the limit as z approaches real infinity is defined and the dual is $S^{-1} (-S (z - t_0)) + t_0 = 0$ which is exactly halfway between the two fixed points of -1 and 1. Hope you enjoy working with the alternating sum of the htan function, which is both 2-periodic, and Pi*I periodic, with singularities at Pi*I/2 and 1+Pi*I/2. - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/22/2013, 12:52 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by tommy1729 - 06/22/2013, 08:43 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/22/2013, 09:55 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/23/2013, 11:13 AM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/23/2013, 10:20 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/24/2013, 04:09 PM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by Gottfried - 06/25/2013, 10:45 AM RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/25/2013, 01:37 PM

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