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The upper superexponential
#15
(05/11/2009, 01:21 PM)bo198214 Wrote: is entire, has period .
is not entire, has period .
....
They have no limit along the imaginary axis because they are imaginary periodic.
When I first looked at Dimitrii's graphs in "Bummer", I didn't realize that the two functions were completely different functions in the imaginary plane, and have different imaginary periods! What I noticed was one had cut points, and the other had fractal behavior. Are the imaginary periods exactly repeating copies?

(05/10/2009, 02:13 PM)Kouznetsov Wrote: Functions above are related: can be expressed through and can be expressed through with some complex constant ofsets of the arguments.

The fractal behavior of is increasing to infinity via tetration, except it is occurring at the i=imaginary_period/2 line, with real values! But otherwise, the fractal behavior is as one would expect! It sounds as though the conversions are as simple as:



,

Where the complex offset is just a real offset plus half of the imaginary period of each function.
This means along with the complex offsets, also allows conversions between and , the lower superexponential, and the upper superexponential.
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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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