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 Universal uniqueness criterion? Kouznetsov Fellow Posts: 151 Threads: 9 Joined: Apr 2008 06/23/2009, 02:57 AM (06/22/2009, 09:46 PM)bo198214 Wrote: I asked you som time ago to apply your algorithm to other fixed points, but you somehow did not follow that path.Assume that for another tetration $F$, we have some probe function $E(y)=F(iy)$ for real $y$; id est, along the imaginary axis. Assume, Function $E$ is suposed to go to $L_m$ at infinity and $L_m^*$ at minus infinity; $\log(L_m)=L_m+2\pi i m$, and $m$ is integer constant. In order to adjust the probe function to some tetration, we need to evaluate the contour integral. If we use the same contour as in the paper http://www.ams.org/mcom/2009-78-267/S002.../home.html then we need the values at $1+i y$ and $-1+iy$ for real $y$. It is easy to estimate values at $1+i y$; use estimate $\exp(E(y))$. As for $-1+i y$; we use estimate $\log(E(y))+2\pi i m$ for positive $y$ and $\log(E(y))-2\pi i m$ for negative $y$. Either we have singularity (jump) at $-1$, or $m=0$. This explains, why I did not construct such "another tetration", but this is not a proof that this is impossible. Suggest the holomorphic probe function to begin with. Such a function should have some smooth kink of the phase, in order to avoid the jump; but allow such a jump for the principal branch of its logarithm. Then we can run the same algorithm, with additional control of the branch of the logarithm. Such a control should recover $F(-1+iy)=\log(F(iy))+i\pi m$, adding unity or minus unity to $m$ each time when $E(y)$ passes through negative real values. We need the holomorphic kinky probe function, then we can run the algorithm to recover the kinky tetration. I think about something like $E(y)= \Re(L_1) +(1-\Re(L_1))/ \cosh(y) + \Im(L_1) \tanh(y)$ « Next Oldest | Next Newest »

 Messages In This Thread Universal uniqueness criterion? - by bo198214 - 05/21/2008, 06:24 PM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 05:19 AM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 06:42 AM RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 11:25 AM RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 03:11 PM RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 05:55 PM RE: Universal uniqueness criterion? - by bo198214 - 05/23/2008, 12:07 PM RE: Universal uniqueness criterion? - by Gottfried - 06/25/2008, 06:15 AM Uniqueness of analytic tetration - by Kouznetsov - 09/30/2008, 07:58 AM RE: Uniqueness of analytic tetration - by bo198214 - 09/30/2008, 08:17 AM RE: Universal uniqueness criterion? - by bo198214 - 10/04/2008, 11:19 PM RE: Universal uniqueness criterion? - by Kouznetsov - 10/05/2008, 12:22 AM RE: Universal uniqueness criterion? - by Kouznetsov - 06/19/2009, 08:45 AM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 02:04 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 02:51 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 04:19 PM RE: miner error found in paper - by bo198214 - 06/19/2009, 04:53 PM i don't think it will work - by Base-Acid Tetration - 06/19/2009, 05:17 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 06:25 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/19/2009, 06:27 PM RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 07:59 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/20/2009, 02:01 PM RE: Universal uniqueness criterion? - by bo198214 - 06/20/2009, 02:10 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 02:39 PM RE: Universal uniqueness criterion? - by Kouznetsov - 06/23/2009, 05:46 PM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 09:28 PM RE: Universal uniqueness criterion? - by Kouznetsov - 06/24/2009, 05:02 AM RE: Universal uniqueness criterion? - by Base-Acid Tetration - 07/04/2009, 11:17 PM RE: Universal uniqueness criterion? - by Kouznetsov - 07/05/2009, 08:28 AM RE: Universal uniqueness criterion? - by bo198214 - 07/05/2009, 06:54 PM

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