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The upper superexponential
#7
bo198214 Wrote:....
Unfortunately the convergence gets quite bad for approaching , so I could not really check numerically.
On the other hand Walker describes also two solutions for 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 .
....
in the thread regular slog.
Literature is: Szekeres "Regular iteration of real and complex functions."
Kouznetsov has graphs of the lower super exponential for 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 , the function exponentially decays to its limiting value in the complex plane at +/- i . This is probably also true for the upper super exponential for , as the value at the real axis increases ...
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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

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