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- ...function]] that expresses the [[fixed point]]s of [[logarithm]] to complex base. for base \(b\!=\!\exp(z)\).4 KB (572 words) - 20:10, 11 August 2020
- : \( \mathrm{Sinc}(z)= 1-\frac{z^2}{6}+\frac{z^4}{120}-\frac{z^6}{5040}+ : \(\!\!\!\!\!\!\!\! \mathrm{ArcSinc}(1\!-\!t)= \sqrt{6 t} \left(4 KB (563 words) - 18:27, 30 July 2019
- \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) f(x) \approx x^\nu \left( \frac{2^{-\nu}}{\mathrm{Factorial}(\nu)}+ O(x^2) \right)\)13 KB (1,592 words) - 18:25, 30 July 2019
- ...tion of the [[superfunction]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed point \(L\!=\!4\). 0.12022125769065893274e-1, 0.45849888965617461424e-2,1 KB (139 words) - 18:48, 30 July 2019
- ...tion of the [[Abel function]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed point \(L\!=\!4\). -0.587369764200886206e-2, 0.289686728710575713e-2,2 KB (163 words) - 18:47, 30 July 2019
- Consider [[logarithm]] to base \(~s~\) from both sides of equation (1), assuming that \(~s~\) and \(~g(z)~ (2) \(~ ~ ~ \log_s\Big(~ g\big( T(z)\big)~\Big) = 1 + \log_s\big(g(z)\big)~\)8 KB (1,239 words) - 11:32, 20 July 2020
- (2) \(~ ~ ~ g\big(T(z)\big)= K \, g(z) \) http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html10 KB (1,627 words) - 18:26, 30 July 2019
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
