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Create the page "Base sqrt(2)" on this wiki! See also the search results found.
- [[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
File:QexpMapT400.jpg [[Complex map]] of function $\sqrt(\exp)= \exp^{1/2}$, [[Halfiteration]] of [[exp]]onential to base $\mathrm e$.(1,881 × 1,881 (1.83 MB)) - 18:26, 11 July 2013- https://www.morebooks.de/store/gb/book/superfunctions/isbn/978-620-2-67286-3 [[File:978-620-2-67286-3-full.jpg|440px]]15 KB (2,166 words) - 20:33, 16 July 2023
File:IterEq2plotT.jpg [[Explicit plot]] of $n$th [[iteration]] of [[exponential]] to [[base sqrt(2)]] for various values of the number $c$ of iterations. ...tation through the [[superfunction]] $F$ of the exponential to base $\sqrt{2}$, constructed at the fixed point $L\!=\!4$, and the corresponding [[Abel f(2,922 × 2,922 (1.35 MB)) - 08:38, 1 December 2018
File:Ack3a600.jpg [[Complex map]] of [[tetration]] to base $b\!=\!\sqrt{2}\!\approx\!1.41$ for(m=-30;m<31;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}(5,130 × 1,793 (1.09 MB)) - 08:28, 1 December 2018
File:Ack3c600.jpg [[Complex map]] of [[tetration]] to base $b\!=\!3/2\!=1.5$ for(m=-30;m<31;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}(5,130 × 1,776 (1.5 MB)) - 08:28, 1 December 2018
File:Ack4c.jpg [[Complex map]] of [[tetration to Sheldon base]] $b\!=\! cu=.5-I/(2.*M_PI)*log( (z_type(1.,-A)+z)/(z_type(1., A)-z) );(5,130 × 1,760 (1.92 MB)) - 08:28, 1 December 2018
File:E1e14z600.jpg $b=\sqrt{2}$, bottom plot. //b=r=2.71(3,566 × 6,300 (1.85 MB)) - 08:34, 1 December 2018
File:Esqrt2ite12mapT80.jpg [[Complex map]] of the 1/2 [[iterate]] of the [[exponential to base sqrt(2)]], which is $T(z)= \exp_{\sqrt{2}}(z)=\big(\sqrt{2}\big)^z$(2,302 × 2,322 (1.41 MB)) - 08:35, 1 December 2018
File:Esqrt2ite13MapT80.jpg [[Complex map]] of the 1/3 [[iterate]] of the [[exponential to base sqrt(2)]], which is $T(z)= \exp_{\sqrt{2}}(z)=\big(\sqrt{2}\big)^z$(2,302 × 2,322 (1.86 MB)) - 08:35, 1 December 2018
File:Expe1eplotT.jpg [[Explicit plot]] of [[exponential]] to [[base e1e]] (thick green curve) and that of the [[exponential]] to [[base sqrt2]] (thin red curve)(2,515 × 1,751 (350 KB)) - 08:35, 1 December 2018
File:Expq2mapT1000.jpg [[Complex map]] of [[exponential to base sqrt2]] $u+\mathrm i v=\exp_{\sqrt{2}}(x+\mathrm i y)$(2,333 × 2,333 (1.8 MB)) - 08:35, 1 December 2018
File:Loge1emapT1000.jpg [[Complex map]] of [[logarithm]] to [[base sqrt2]], $b=\sqrt{2}\approx 1.41421356237$; $u+\mathrm i v=\log_{\sqrt{2}}(x+\mathrm i y)$(2,361 × 2,333 (1.67 MB)) - 08:41, 1 December 2018
File:Logq2mapT1000.jpg [[Complex map]] of [[logarithm]] to [[base sqrt2]], $b=\sqrt{2}\approx 1.41421356237$; $u+\mathrm i v=\log_{\sqrt{2}}(x+\mathrm i y)$(2,361 × 2,333 (1.49 MB)) - 08:42, 1 December 2018
File:Sqrt23uplot.jpg Explicit plot of the growing superexponential to base $\sqrt{2}$ , thick curve, and the exponential to this base, thin curve:(1,569 × 4,381 (240 KB)) - 08:52, 1 December 2018
File:Sqrt27t.jpg [[Explicit plot]] of [[tetration]] to base $\sqrt{2}$ $y=\mathrm{tet}_{\sqrt{2}}(x)$(3,401 × 3,401 (475 KB)) - 08:52, 1 December 2018
File:Sqrt27u.png ...roximate symmetry of the [[explicit plot]] of [[tetration]] to base $\sqrt{2}$ in figure http://mizugadro.mydns.jp/t/index.php/File:Sqrt27t.jpg $y=\mathrm{devi}(x)=\mathrm{tet}_{\sqrt{2}}(x) + \mathrm{ate}_{\sqrt{2}}(-x) ~$(856 × 507 (50 KB)) - 08:52, 1 December 2018
File:Sqrt2atemap.jpg [[Complex map]] of [[arctetration]] to base $\sqrt{2}$: $u\!+\!\mathrm i v = \mathrm{ate}_{\sqrt{2}}(x\!+\!\mathrm i y)$(1,758 × 1,741 (723 KB)) - 08:52, 1 December 2018
File:Sqrt2diimap80.jpg ...exponent to base $\sqrt{2}$ constructed at its lower ("down") fixed point 2: $u\!+\!\mathrm i v= \exp_{\sqrt{2},\mathrm d}(x\!+\!\mathrm i y)$(2,302 × 2,306 (1.27 MB)) - 08:52, 1 December 2018
File: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 2018
