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Create the page "Tetration to real base" on this wiki! See also the search results found.
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
File:B271a.png [[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
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
File:E1etetma8.jpg [[Complex map]] of [[tetration]] to [[base e1e]] [[Tetration]] $F=\mathrm{tet}_{\eta}$ is real-holomorphic solution of equation(4,472 × 3,320 (1.69 MB)) - 08:34, 1 December 2018
File:Shelima600.png Explicit plot of real and imaginary part of [[tetration to Sheldon base]] of imaginary argument. should be loaded in order to compile the code below:(1,693 × 531 (83 KB)) - 08:51, 1 December 2018
File:Shelr80.png Explicit plot of [[tetration to Sheldon base]] for real values of the argument. For comparison, the black line shows the graphic for real base $b=1.5$, id est, $y=\mathrm{tet}_{1.5}(x)$(1,563 × 1,454 (237 KB)) - 08:51, 1 December 2018
File:Shelre60.png Explicit plot of [[tetration to Sheldon base]] for real values of the argument. should be loaded in order to compile the code below:(1,172 × 1,090 (142 KB)) - 08:51, 1 December 2018
File:Sqrt2sufuplot.png Four superexponentials to base \(b=\sqrt{2}\) They are real-holomorphic solutions \(F\) of the transfer equation(3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022
File:Tet5loplot.jpg Graphical search for the real [[fixed point]]s of [[tetration]]: $\mathrm e\!=\!\exp(1)\!\approx\!2.71$ is base of the natural logarithm,(1,477 × 1,486 (283 KB)) - 08:53, 1 December 2018
File:TetsheldonmapT600.jpg [[Complex map]] of [[Tetration]] to the [[Sheldon base]] $b= 1.52598338517 + 0.0178411853321\, \mathrm i$. Constants $L_1$ and $L_2$ are [[fixed point]]s of logarithm to base $b$; they are determined (and evaluated) through function [[filog]]:(5,130 × 1,776 (1.02 MB)) - 08:54, 1 December 2018
