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File:E1eSuMap600.jpg [[Complex map]]s of two superexponentials to the [[Henryk base]] for [[tetration]] $F\!=\! \mathrm{tet}_\eta$(3,377 × 5,055 (1.37 MB)) - 08:34, 1 December 2018File: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 2018File:E1eti4.jpg [[Complex map]] of [[arctetration]] to [[base e1e]], $\eta=\exp(1/\mathrm e)$ fprintf(o,"101 151 translate\n 10 10 scale\n");(2,236 × 1,660 (1.02 MB)) - 08:34, 1 December 2018File:Shelima600.png Explicit plot of real and imaginary part of [[tetration to Sheldon base]] of imaginary argument. -10.00 2.2202212609 -1.3393771522(1,693 × 531 (83 KB)) - 08:51, 1 December 2018File: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 2018File: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 2018File:Sqrt27u.png ...k of the approximate symmetry of the [[explicit plot]] of [[tetration]] to base $\sqrt{2}$ in figure http://mizugadro.mydns.jp/t/index.php/File:Sqrt27t.jpg http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>(856 × 507 (50 KB)) - 08:52, 1 December 2018File:Sqrt2atemap.jpg [[Complex map]] of [[arctetration]] to base $\sqrt{2}$: http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>(1,758 × 1,741 (723 KB)) - 08:52, 1 December 2018File:Sqrt2diimap80.jpg [[Complex map]] of iterate number i of exponent to base $\sqrt{2}$ constructed at its lower ("down") fixed point 2: http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>(2,302 × 2,306 (1.27 MB)) - 08:52, 1 December 2018File:Sqrt2eitet.jpg [[iterate]]s of the [[esponent]] to base $\sqrt{2}$, constructed with [[tetration]] and [[arctetration]] to thie base.(3,051 × 3,022 (1.36 MB)) - 08:52, 1 December 2018File:Sqrt2q2map600.jpg [[Complex map]] of the half iterate of exponent to base $\sqrt{2}$ regular at its lowest fixed point. This function is expressed through [[tetration]] and [[arctetration]] to base $\sqrt{2}$:(1,766 × 1,750 (1.43 MB)) - 08:52, 1 December 2018File:Sqrt2srav.png Comparison or two half iterate of exponent to base \( \sqrt{2} \) constructed at fixed point 2 and at fixed point 4. scaled with factor \(10^{24} \).(2,532 × 1,639 (263 KB)) - 10:53, 24 June 2020File:Sqrt2sufuplot.png Four superexponentials to base \(b=\sqrt{2}\) scaled with factor \(10^{24} \) is shown with violet sinusoidal bell.(3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022File:Sqrt2tetatemap.jpg for the [[tetration]] and [[arctetration]] to base $\sqrt{2}$(1,758 × 1,741 (1,008 KB)) - 08:52, 1 December 2018File:Sqrt2tetmap.jpg [[Complex map]] of [[tetration]] to base $\sqrt{2}$: http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>(1,758 × 1,741 (656 KB)) - 08:52, 1 December 2018File:Sqrt2uiimap80.jpg [[Complex map]] of iterate number i of exponent to base $\sqrt{2}$ constructed at its upper fixed point 4: http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>(2,302 × 2,306 (1.84 MB)) - 08:52, 1 December 2018File: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 2018File: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 2018File:Tetsheldonzoo.jpg [[Complex map]] of [[tetration to Sheldon base]], zoom-in from the central part of figure should be loaded in order to compile the code below(4,337 × 4,317 (1.73 MB)) - 08:54, 1 December 2018- [[Base e1e]] refers to the value of base \(b= \eta =\exp(1/\mathrm e)\approx 1.4446678610\) ...corresponding [[exponential]], [[SuperExponential]] (in particular, the [[tetration]]) and the inverse functions.4 KB (559 words) - 17:10, 10 August 2020