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 Dmitrii Kouznetsov's Tetration Extension bo198214 Administrator Posts: 1,395 Threads: 91 Joined: Aug 2007 05/23/2008, 05:52 PM Kouznetsov Wrote:Bo, namely for $b=\sqrt{2}$ my expression can be simplified to yours. Yes you are right, again stupid mistake of mine. For $b=\sqrt{2}$ the fixed point is $a=2$ and the period is $\frac{2\pi i}{\ln(\ln(a))}=\frac{2\pi i}{\ln(\ln(2))}\approx -17.1431*I$. Good, so seems quite as if tetration by regular iteration gives the same as tetration with your approach. As it is too expensive to compute the contours, I give here pictures of the regular tetration as 3d plot, absolute value over the complex plane, here it is: over -1-I*10 ... +1+I*10     over 0 ... 1+I*20     One can clearly see the period of -17.14 along the imaginary axis. Quote:Quote:Btw. there are infinitely many analytic functions that have no singularity on right halfplane: If $F$ has no singularity there, also $F(x+c\sin(2\pi x))$, $0, is a superexponential with no singularities on the right halfplane and any 1-periodic function $p$ with $p(x)>-x$ in $0 would do. I disagree. At some smooth contour $u$ in your strip, the contour $v=u+c \sin(2\pi u)$ enters the left halfplane and crosses the cut $v<-2$. You have no need to evaluate any tetration in order to see it. Corresponding contour $F(v)$ is not continuous. You are right. As sin is not bounded in the real part on the strip it can go to arbitrary negative values. Quote:Fig.2 is ready at http://en.citizendium.org/wiki/Tetration...rameters00. Try to run it. ok, that works too (but as a c++ program, which I wasnt aware of). « Next Oldest | Next Newest »

 Messages In This Thread Dmitrii Kouznetsov's Tetration Extension - by andydude - 04/16/2008, 10:16 PM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 04/21/2008, 10:41 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 04/22/2008, 12:59 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 04/22/2008, 08:18 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 04/24/2008, 01:02 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 04/25/2008, 04:06 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 04/26/2008, 02:12 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 04/26/2008, 06:26 PM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/17/2008, 03:22 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/18/2008, 05:31 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/18/2008, 05:09 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/21/2008, 12:20 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/21/2008, 06:22 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/21/2008, 11:18 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/22/2008, 07:12 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/22/2008, 10:43 PM RE: Dmitrii Kouznetsov's Tetration Extension - by andydude - 05/22/2008, 10:59 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/22/2008, 11:36 PM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/23/2008, 06:21 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/23/2008, 08:48 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/23/2008, 10:09 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/23/2008, 02:15 PM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/23/2008, 03:47 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/23/2008, 04:35 PM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/23/2008, 05:52 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/23/2008, 11:03 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/24/2008, 05:36 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/24/2008, 09:43 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/24/2008, 09:53 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/24/2008, 11:24 AM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/24/2008, 11:39 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/24/2008, 12:08 PM RE: Dmitrii Kouznetsov's Tetration Extension - by bo198214 - 05/26/2008, 07:01 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/26/2008, 09:03 AM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/27/2008, 03:58 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 05/28/2008, 08:58 AM compare complex plot with matrix power method - by bo198214 - 10/09/2008, 10:21 PM RE: Dmitrii Kouznetsov's Tetration Extension - by Kouznetsov - 10/10/2008, 01:17 AM [split] Taylor series of upx function - by Kouznetsov - 11/20/2008, 01:31 AM

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