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SuZex
Let $~ x_n$ be real solution of equation $F_n(x_n)=1$. ...th, similar to that of the [[SuperFactorial]] and that of [[tetration]] to base $b>\exp^2(-1)=\exp(1/\mathrm e)$.

7 KB (1,076 words) - 18:25, 30 July 2019
SuZex approximation
...imations of [[SuZex]] with elementary functions. All the maps are supposed to be displayed in the same scale. ...positive part of the real axis. The superfunction $F=\mathrm{SuZex}$ is real–holomorphic; $F(z^*)=F(z)^*$,

14 KB (2,037 words) - 18:25, 30 July 2019
Schroeder equation
where function $~T~$ is supposed to be given, while constant $s$ and function$~g~$ should be constructed. ...er equation]]; the solutions (called [[Schroeder function]]s ) are related to the [[superfunction]]s and the [[Abel function]]s.

8 KB (1,239 words) - 11:32, 20 July 2020
File:Ater01.png
[[ArcTetration]] to various values of base $b$ at real values of the argument. [[Category:Tetration]]

(1,192 × 1,096 (174 KB)) - 08:30, 1 December 2018

[[Complex map]] of [[ArcTetration]] to base $\mathrm e \approx 2.71~$: The ArcTetration $\mathrm{ate}$ is inverse of [[tetration]] and holomorphic solution of the [[Abel equation]]

(1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018

File:B271t.png

[[Complex map]] of tetration to base $\mathrm e$, isolines of real and imaginary parts of $v\!=\!\Im(f)\!=\!\mathrm {const}$ are plotted; integer values correspond to the thick lines.

(1,609 × 1,417 (791 KB)) - 08:30, 1 December 2018

File:ExpQ2mapT.png

[[Complex map]] of [[exponential]] to [[base sqrt2]], id est, $b=\sqrt{2}$; ...!1$, $u\!=\!2$, $u\!=\!4$, $u\!=\!8$ passthrough the integer values at the real axis.

(1,765 × 1,729 (1.15 MB)) - 08:35, 1 December 2018

File:Filogbigmap100.png

$\mathrm{Filog}(z)$ expresses the [[fixed point]] of [[logarithm]] to base $b\!=\!\exp(z)$. Another fixed point to the same base can be expressed with

(2,870 × 2,851 (847 KB)) - 08:36, 1 December 2018

File:Filogmap300.png

$\mathrm{Filog}(z)$ expresses the [[fixed point]] of [[logarithm]] to base $b\!=\!\exp(z)$. Another fixed point to the same base can be expressed with

(893 × 897 (292 KB)) - 09:40, 21 June 2013

File:LogQ2mapT2.png

[[Complex map]] of [[logarithm]] to base $b\!=\!\sqrt{2}$; ...1$, $u\!=\!2$, $u\!=\!4$, $u\!=\!6$ pass through the integer values at the real axis.

(1,765 × 1,729 (1.43 MB)) - 09:43, 21 June 2013

File:Tet10bxr.jpg
[[Explicit plot]] of [[tetration]] for real values of base $b\!>\!1$. should be loaded in order to compile the code below

(2,491 × 1,952 (236 KB)) - 08:53, 1 December 2018

File:TetSheldonImaT.png

Few iterations at the [[Iterated Cauchi]] for the [[Tetration to Sheldon base]]. The solution $F$ is supposed to have the specific boundary behavior:

(4,359 × 980 (598 KB)) - 09:40, 21 June 2013

File:TetSheldonTestImaT.png

Test of the evaluation of the [[tetration to Sheldon base]] should be loaded in order to compile the [[C++]] code below:

(4,318 × 980 (322 KB)) - 08:53, 1 December 2018

Maps of tetration
[[File:Ack3a600.jpg|400px|thumb|Base $b=\sqrt{2}\approx 1.41$]] [[File:Ack3b600.jpg|400px|thumb|Henryk base, $b=\exp(1/\mathrm e)\approx 1.44$]]

5 KB (761 words) - 12:00, 21 July 2020
Superfunctions
In particular, results for [[tetration]], [[arctetration]] and [[iterate]]s of [[exponential]] are presented. Explicit plot: [[tetration]].

15 KB (2,166 words) - 20:33, 16 July 2023

File:Ackerplot.jpg

[[Explicit plot]] of the 5 [[Ackermann function]]s to base $\mathrm e$ $A_{\mathrm e,4}(z)=\mathrm{tet}(z)~$ , see [[natural tetration]]

(2,800 × 4,477 (726 KB)) - 08:28, 1 December 2018

File:Ackerplot400.jpg

[[Explicit plot]] of the 5 [[Ackermann function]]s to base $\mathrm e$ $A_{\mathrm e,4}(z)=\mathrm{tet}(z)~$ , see [[natural tetration]]

(3,355 × 4,477 (805 KB)) - 08:29, 1 December 2018

File:Analuxp01t400.jpg

...d $v$ are [[logamplitude]] and [[phase]] of the plotted functions; not the real and imaginary parts, as usually. ...rresponds to the displacement of the map for unity to the right, along the real axis.

(2,083 × 3,011 (1.67 MB)) - 08:29, 1 December 2018