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Dmitrii Kouznetsov's Tetration Extension
#4
Kouznetsov Wrote:By the way, your deduction gives the hint, how to prove the Theorem 1.

Perhaps. I am not convinced yet that it is true, but if it was, this would be great. We even know vice versa if we have two solutions and of the Abel equation then , meaning that is a 1-periodic function, so we know already that each other solution of the Abel equation must be of the form for some 1-periodic . To prove theorem 1 everything depends on the behaviour of those 1-periodic functions for . For uniqueness roughly the real value must be go to infinity for the imaginary argument going to infinity.

Quote:(However, we have to scale the argument of sin function.)

Corrected in the original post.

Quote: How about the collaboration?
That would be great.

Quote:(P.S. Does the number of replies I should answer grow as the Ackermann function of time, or just exponentially?)

I would guess its rather logarithmically (much questions at the start but then slowly ebbing away)! At least here is another question: Can you please compute values on the real axis for bases for example for ? I would like to compare your solution with the regular tetration developed at the lower real fixed point (which would be 2 in the case of ) of .

@Andrew
Can you post a comparison graph with your slog/sexp? The values are in Dmitrii's paper. How does the periodicity of your slog (or was it sexp?) at the imaginary axis compare with Dmitrii's limit (where is a fixed point of )?
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RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 04/22/2008, 08:18 AM

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