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 complex base tetration program Gottfried Ultimate Fellow Posts: 761 Threads: 118 Joined: Aug 2007 10/24/2016, 11:50 PM (This post was last modified: 10/24/2016, 11:54 PM by Gottfried.) Hi Sheldon - inspired by the bugs, rooted in interferences between the procedures in fatou.gp and my std-user-library I was also reviewing the older tetcomplex.gp procedure which you've posted earlier (and which worked in my environment with very little renaming-conventions), and did also some minor edits for numerical improvements (replaced "eval"-procedures by "subst") and deleted all "kill(x)"-calls. Using the base $\small B=2$ I could nicely reproduce the problem in MSE: does exist and then what is $\small x \gt 2$ in $\;^2x = \;^x2$ By some other idea I investigated the behave near above the real axis, and specifically I looked at the point $\small z_0= \text{Re} (L) + \varepsilon I$ and found, that the required height $h$ to iterate from $z_0$ to$L$ is nearly $\small 2 \pi I$ , so $\small \text{sexp}(2 \pi I+ \text{slog}(z_0 ) )\approx L \qquad \qquad \text{ using }z_0 \text{ with } \varepsilon=1e-6,1e-12,1e-24,...$ That this is very near suggests, that here equality is intended (and it is also different from the Schröder-method). However, the error is in the near of 0.003 which looks large in comparision to the numerical accuracy for other computations (20 to 30 digits correct by my initialization) . Could that result be improved by some finetuning? (Or did I speculate wrongly?) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread complex base tetration program - by sheldonison - 02/29/2012, 10:28 PM RE: complex base tetration program - by Kouznetsov - 02/29/2012, 11:49 PM RE: complex base tetration program - by sheldonison - 03/01/2012, 12:09 AM RE: complex base tetration program - by sheldonison - 03/01/2012, 10:34 AM RE: complex base tetration program - by Kouznetsov - 03/01/2012, 12:04 PM RE: complex base tetration program - by sheldonison - 03/01/2012, 03:47 PM RE: complex base tetration program - by sheldonison - 03/02/2012, 09:20 AM RE: complex base tetration program - by sheldonison - 03/07/2012, 12:08 AM RE: complex base tetration program - by sheldonison - 03/07/2012, 06:08 PM RE: complex base tetration program - by sheldonison - 03/08/2012, 09:51 PM RE: complex base tetration program - by mike3 - 03/10/2012, 06:59 AM RE: complex base tetration program - by sheldonison - 03/10/2012, 08:53 PM RE: complex base tetration program - by mike3 - 03/11/2012, 12:27 AM RE: complex base tetration program - by sheldonison - 03/12/2012, 04:20 AM RE: complex base tetration program - by sheldonison - 03/16/2012, 07:42 PM RE: complex base tetration program - by Gottfried - 02/06/2016, 01:37 AM RE: complex base tetration program - by sheldonison - 02/06/2016, 04:04 PM RE: complex base tetration program - by Gottfried - 02/06/2016, 05:36 PM RE: complex base tetration program - by Gottfried - 02/07/2016, 05:27 AM RE: complex base tetration program - by sheldonison - 02/07/2016, 12:28 PM RE: complex base tetration program - by Gottfried - 02/07/2016, 01:25 PM RE: complex base tetration program - by Gottfried - 10/24/2016, 11:50 PM RE: complex base tetration program - by sheldonison - 10/26/2016, 08:01 AM RE: complex base tetration program - by Gottfried - 10/26/2016, 10:02 AM

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