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The upper superexponential
#10
bo198214 Wrote:As it is well-known we have for
the regular superexponential at the lower fixed point.

This can be obtained by computing the Schroeder function at the fixed point of .
.....
Now the upper regular superexponential is the one obtained at the upper fixed point of .
For this function we have however always ,
so the condition can not be met.
Instead we normalize it by , which gives the formula:

The "upper/lower" properties of these two sexp solutions are very interesting, especially being able to convert one to the other. The "upper" solution approaches the larger fixed point at -infinity, and the lower solution approaches the smaller fixed point at +infinity.

Can this be applied to Kneser's fixed point solution for bases larger than (e^(1/e))? For base e, Kneser's solution, has complex values at the real number line, and the function approaches the fixed point as x grows towards +infinity. But the desired solution has real values for all x>-2, and complex values for all x<-2 (except for the singularities). Moreover, the desired solution approaches the fixed point, as real x approaches -infinity.

This has probably already been done, but can Kneser's base e solution, approaching a complex fixed point at +infinity, be converted it to another solution, approaching the fixed point at -infinity, with real values at the real number line, for all x>-2? Perhaps this line of reasoning isn't applicable because the resulting solution, approaching the fixed point at -infinity, probably would not have imaginary values of zero for for real all x>-2.
- Sheldon
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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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