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File:Filogmap300.png ...the branchpoint $z=1/\mathrm e$; the second goes through the point $z=\pi/2$, where the fixed points are $\pm \mathrm i$. ...the cut, the function has real values; in particular, at $z=\ln\big(\sqrt{2}\big)$, there values are integer(893 × 897 (292 KB)) - 09:40, 21 June 2013
File:FourierExampleGauss16pol04Ta.png $y=A(x)=\exp(-x^2/2) x^2(-3+x^2)$ versus $x$, dashed curve; ...rete presentaton with array of length $N=16$ with step $\mathrm {d}x=\sqrt{2 \pi/N} \approx0.626657$ , the $A$ is practically overlapped with the eval(2,134 × 470 (88 KB)) - 09:39, 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:IterPowPlotT.png ...Iteration of the quadratic function, id est, [[power function]] for power 2; $y=\mathrm{Pow}_2^{~c}(z)=T^c(x)~$ for various values of number $c$ of ite ...!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$(2,093 × 2,093 (680 KB)) - 20:50, 28 September 2013
File:LambertWmap150.png z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t); if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);(1,773 × 1,752 (523 KB)) - 08:41, 1 December 2018
File:LambertWplotT.png z_type LambertWe(z_type z){ int n,m=100; z_type t=1./M_E+z; t*=2*M_E; t=sqrt(t); if( abs(z)<.2 ) return LambertWo(z);(1,267 × 839 (81 KB)) - 09:43, 21 June 2013
File:Logi2c3T1000.png C3=2. /((1.-Q)*(1.-Q2) C5=2.*(7.+Q*(3.+Q*2.)) /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4(1,772 × 1,758 (1.36 MB)) - 08:41, 1 December 2018
File:Logi2c4T1000.png C3=2. /((1.-Q)*(1.-Q2) C5=2.*(7.+Q*(3.+Q*2.)) /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4(1,772 × 1,758 (1.39 MB)) - 08:41, 1 December 2018
File:Logi5T1500.png fprintf(o,"62 2 translate\n 20 20 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n");(3,404 × 540 (185 KB)) - 06:28, 10 June 2022
File:Logi5U1500.png fprintf(o,"1 setlinejoin 2 setlinecap\n"); for(n=-1;n<2;n++){ M( -3,n)L(5,n)}(3,404 × 955 (403 KB)) - 06:30, 10 June 2022
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:PowIteT.jpg ...Iteration of the quadratic function, id est, [[power function]] for power 2; $y=\mathrm{Pow}_2^{~c}(z)=T^c(x)~$ for various values of number $c$ of ite ...!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$(2,093 × 2,093 (1.01 MB)) - 08:46, 1 December 2018
File:QFacMapT.png [[Complex map]] of function [[Square root of factorial]], $\sqrt{\,!\!}$, id est $f(z)=\mathrm{Factorial}^{1/2}(z)$(1,412 × 1,395 (1.47 MB)) - 09:43, 21 June 2013
File:QFactorialQexp.jpg Functions sqrt(!) , left, and sqrt(exp), right, in the complex plane. For <math>c=1/2</math> this expression determines the function <math>\sqrt{H}</math>.(800 × 399 (121 KB)) - 17:23, 11 July 2013
File:SelfCosFTt200.png : $ \displaystyle f_0(x)=\exp(-x^2/2)$ : $ \displaystyle f_1(x)=\exp(-x^2/2) (x^4-3x^2)$(1,467 × 637 (100 KB)) - 09:42, 21 June 2013
File:ShokaMapT.png fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=.8;q=.5; for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".01 W 0 .6 0 RGB S\n");(1,773 × 1,752 (992 KB)) - 08:51, 1 December 2018
File:ShokoMapT.png fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=.6;q=.5; for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".01 W 0 .6 0 RGB S\n");(1,773 × 1,752 (964 KB)) - 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
