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regular tetration base sqrt(2) : an interesting(?) constant 2.76432104
#8
(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 would denote the Kneser-method iteration from x using height h, then in our case with base = sqrt(2)...
Gottfried
The 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 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

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RE: regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 - by sheldonison - 06/25/2013, 01:37 PM

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