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 The upper superexponential sheldonison Long Time Fellow Posts: 683 Threads: 24 Joined: Oct 2008 04/05/2009, 12:45 PM (This post was last modified: 04/05/2009, 04:35 PM by sheldonison.) bo198214 Wrote:.... Unfortunately the convergence gets quite bad for $b$ approaching $e^{1/e}$, so I could not really check numerically. On the other hand Walker describes also two solutions for $b=e^{1/e}$ in "On the solutions of an Abelian equation". I did not really read this article, but I think he also showed that these solutions are not the limit of approaching $e^{1/e}$. .... in the thread regular slog. Literature is: Szekeres "Regular iteration of real and complex functions."Kouznetsov has graphs of the lower super exponential for $b=e^{1/e}$ in the citizendium wiki. He says "the function approaches its limiting value e, almost everywhere". I haven't seen any graphs for the upper superexponential though. For $b>e^{1/e}$, the function exponentially decays to its limiting value in the complex plane at +/- i $\infty$. This is probably also true for the upper super exponential for $b=e^{1/e}$, as the value at the real axis increases ... « Next Oldest | Next Newest »

 Messages In This Thread The upper superexponential - by bo198214 - 03/29/2009, 11:23 AM RE: The upper superexponential - by andydude - 03/31/2009, 04:29 AM RE: The upper superexponential - by sheldonison - 04/03/2009, 03:06 PM RE: The upper superexponential - by bo198214 - 04/03/2009, 04:22 PM RE: The upper superexponential - by sheldonison - 04/05/2009, 12:45 PM RE: The upper superexponential - by bo198214 - 04/06/2009, 06:35 AM RE: The upper superexponential - by Kouznetsov - 05/10/2009, 02:13 PM RE: The upper superexponential - by sheldonison - 05/11/2009, 12:55 PM RE: The upper superexponential - by bo198214 - 05/11/2009, 01:21 PM RE: The upper superexponential - by sheldonison - 05/11/2009, 08:12 PM RE: The upper superexponential - by bo198214 - 05/11/2009, 08:31 PM RE: The upper superexponential - by Kouznetsov - 05/12/2009, 08:54 AM RE: The upper superexponential - by bo198214 - 06/01/2009, 07:24 PM RE: The upper superexponential - by tommy1729 - 04/05/2009, 07:05 PM RE: The upper superexponential - by sheldonison - 04/22/2009, 05:02 PM RE: The upper superexponential - by bo198214 - 04/22/2009, 05:34 PM RE: The upper superexponential/eich-value x for h=0? - by Gottfried - 09/18/2009, 04:01 PM

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