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Create the page "Base sqrt(2)" on this wiki! See also the search results found.

  • File:B271t.png
    [[Complex map]] of tetration to base $\mathrm e$, isolines of real and imaginary parts of DB b=sqrt(2);
    (1,609 × 1,417 (791 KB)) - 08:30, 1 December 2018
  • File:E1efig09abc1a150.png
    [[Complex map]]s of [[tetration]] $\mathrm{tet}_b$ to base<br> $b\!=\!\sqrt{2}$ , right.
    (2,234 × 711 (883 KB)) - 08:34, 1 December 2018
  • File:Esqrt2iterMapT.png
    [[Complex map]] of 1/3 th iteration of the [[exponential]] to [[base sqrt(2)]]. $T(x) = \Big(\sqrt{2}\Big){^z}= \exp_b(z)$
    (1,092 × 1,080 (1.36 MB)) - 09:43, 21 June 2013
  • File:ExpQ2mapT.png
    [[Complex map]] of [[exponential]] to [[base sqrt2]], id est, $b=\sqrt{2}$; $u\!+\!\mathrm i v=\exp_{\sqrt{2}}(x\!+\!\mathrm i y)$
    (1,765 × 1,729 (1.15 MB)) - 08:35, 1 December 2018
  • File:ExpQ2plotT.png
    [[Explicit plot]] of [[exponential]] to base $b\!=\!\sqrt{2} \approx 1.414213562373095$ The [[fixed point]]s $L\!=\!2$ and $L\!=\!4$ are solutions of the equation
    (2,512 × 1,744 (175 KB)) - 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:IterEq2plotU.png
    [[Explicit plot]] of $c$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
    (2,944 × 2,944 (986 KB)) - 21:42, 27 September 2013
  • File:LogQ2mapT2.png
    [[Complex map]] of [[logarithm]] to base $b\!=\!\sqrt{2}$; ...range of holomorphism is marked with dashed line. Lines $u\!=\!1$, $u\!=\!2$, $u\!=\!4$, $u\!=\!6$ pass through the integer values at the real axis.
    (1,765 × 1,729 (1.43 MB)) - 09:43, 21 June 2013
  • File:Sqrt2figf45bT.png
    ...primary expansion of the growing [[superexponential]] to base $b\!=\!\sqrt{2}$ built up at the [[fixed point]] $L\!=\!4$. $T(z)=\exp_{\sqrt{2}}(z)=\Big( \sqrt{2} \Big)^z$
    (2,180 × 2,159 (1.01 MB)) - 08:52, 1 December 2018
  • File:Sqrt2figf45eT.png
    ...omorphic [[superfunction]] $F$ of the [[exponential]] to base $b\!=\!\sqrt{2}$ built up at its fixed point $L\!=\!4$ with condition $F(0)\!=\!5$. The image is almost Figure 2 (left at the bottom) of publication in [[Mathematics of Computation]]
    (2,180 × 2,159 (1.18 MB)) - 08:52, 1 December 2018
  • File:Sqrt2figL45eT.png
    ...] of the [[Abel function]] $G$ of the [[exponential]] to base $b\!=\!\sqrt{2}$ constructed at the fixed point $L\!=\!4$ with normalization $G(0)\!=\!5$. ..., H.Trappmnn. Portrait of the four regular super-exponentials to base sqrt(2).
    (2,180 × 2,159 (1.07 MB)) - 12:53, 20 July 2020
  • File:Tet10bxr.jpg
    [[Explicit plot]] of [[tetration]] for real values of base $b\!>\!1$. { fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
    (2,491 × 1,952 (236 KB)) - 08:53, 1 December 2018
  • 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
  • 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
  • File:Sqrt2q2map600.jpg
    [[Complex map]] of the half iterate of exponent to base $\sqrt{2}$ regular at its lowest fixed point. $u\!+\!\mathrm i v= \exp_{\sqrt{2},\mathrm d}^{~ 1/2}(x\!+\!\mathrm i y)$
    (1,766 × 1,750 (1.43 MB)) - 08:52, 1 December 2018
  • File:Sqrt2srav.png
    ...half iterate of exponent to base \( \sqrt{2} \) constructed at fixed point 2 and at fixed point 4. \( y=\exp_{\sqrt{2},\mathrm u}^{~1/2}(x) \) , solid line
    (2,532 × 1,639 (263 KB)) - 10:53, 24 June 2020
  • File:Sqrt2sufuplot.png
    Four superexponentials to base \(b=\sqrt{2}\) \(F_{2,3} \) and
    (3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022
  • File:Sqrt2tetatemap.jpg
    $\mathrm{tet}_{\sqrt{2}}(\mathrm{ate}_{\sqrt{2}}(z))=z$ and [[arctetration]] to base $\sqrt{2}$
    (1,758 × 1,741 (1,008 KB)) - 08:52, 1 December 2018
  • File:Sqrt2tetmap.jpg
    [[Complex map]] of [[tetration]] to base $\sqrt{2}$: $u\!+\!\mathrm i v = \mathrm{tet}_{\sqrt{2}}(x\!+\!\mathrm i y)$
    (1,758 × 1,741 (656 KB)) - 08:52, 1 December 2018
  • File:Sqrt2uiimap80.jpg
    [[Complex map]] of iterate number i of exponent to base $\sqrt{2}$ constructed at its upper fixed point 4: $u\!+\!\mathrm i v= \exp_{\sqrt{2},\mathrm u}(x\!+\!\mathrm i y)$
    (2,302 × 2,306 (1.84 MB)) - 08:52, 1 December 2018
  • File:Tet5loplot.jpg
    $\mathrm e\!=\!\exp(1)\!\approx\!2.71$ is base of the natural logarithm, $\tau\!\approx\! 1.63532$ is crytical base; at $b\!=\!\tau$, tetration has 2 real fixed points:
    (1,477 × 1,486 (283 KB)) - 08:53, 1 December 2018
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