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 Dmitrii Kouznetsov's Tetration Extension bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/23/2008, 03:47 PM (This post was last modified: 11/20/2008, 09:28 AM by bo198214.) Kouznetsov Wrote:bo198214 Wrote:... I would begin with what I am best with: tetration by regular iteration.It does not click.. May be I find it later.. Regular iteration is definitely something you have to learn about. The usual starting article for doing so is G. Szekeres, Regular iterations of real and complex functions. Acta Math. 100 (195, 203-258 However I think it is written somewhat cumbersome. If you speak French I advice you to read Jean Écalle, Théorie des invariants holomorphes, Publ. Math. Orsay No. 67–7409 Lars Kinderman has a very good collection of literature for the topic. Quote:Quote:And as I already explained, it is periodic along the imaginary axis, hence has no limit at $i\infty$. Does that mean that it is different to your's? No, that does not. The analytic tetrations should coincide. Does your soluiton show period $\frac{2\pi \rm i}{ \ln\big(\ln(\sqrt{2})\Big)+\ln(2)}\approx 17.1431 \!~\rm i$? Hm, not exactly, what I derived some posts earlier would give merely $\frac{2\pi i}{\ln(\ln(\sqrt{2}))}$, yours is $\frac{2\pi i}{\ln(\ln(2))}$. 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. More interesting seems here the boundedness on the strip $0<\Re(z)\le 1$, which seems to be an universal uniqueness criterion. Quote:I made another code for $b=\sqrt{2}$; it does not assume the limiting value. But it knows the asymptotic. ah, ok. Quote:Do you already have writing access at citizendium? Hm, I signed up but did not get any response yet ... Quote:For other users who watch only the last post, I repeat the url: en.citizendium.org/wiki/Usermitrii_Kouznetsov/Analytic_Tetration P.S. At the preview, part of url appears as "smile"; should be U s e r : D m i t r i i _ K o u z n e t s o v without spaces You can include clickable urls into your post with the construction: Code:[url=http://....]how the link appears[/url] « 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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