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• ArcTetration
  ...verse function of [[tetration]], the ArcTetration \( \mathrm {ate}_b \) to base \( b \) satisfies the relations For base \( b\!=\!\mathrm e \!\approx\! 2.71 \), the natural ArcTetration is presented in figure at right with the [[
  7 KB (1,091 words) - 23:03, 30 November 2019
• B271az.cc
  // showing the [[complex map]] of [[ArcTetration]] to base e. // for(m=-2;m<0;m+=2) {M(-4.6,m-.2) fprintf(o,"(%1d)s\n",m);}
  3 KB (529 words) - 14:32, 20 June 2013
• Tania function
  : \(\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \displaystyle (2) ~ ~ ~ Tania function has two [[branch point]]s: \(~ -\!2\!\pm\! \mathrm i \pi~\). The position of the [[cut line]]s depends on the r
  27 KB (4,071 words) - 18:29, 16 July 2020
• Doya function
  : \( \displaystyle \!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \mathrm{Doya}(z)= \mathrm{Tania}\!\Big(1+\mathrm{ArcTania}(z)\Big)\) :\(t\!=\!2\), id est, \(~\mathrm{Doya}^2(x)=\mathrm{Doya}\big(\mathrm{Doya}(x)\big)\)
  19 KB (2,778 words) - 10:05, 1 May 2021
• Table of superfunctions
  : \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \) | \(\displaystyle \frac{-a^2}{z}\)
  11 KB (1,565 words) - 18:26, 30 July 2019
• Square root of exponential
  [[Square root of exponential]] \(\varphi=\sqrt{\exp}=\exp^{1/2}\) is half-iteration of the [[exponential]], id est, such function that its Function \(\sqrt{\exp}\) should not be confused with
  5 KB (750 words) - 18:25, 30 July 2019
• Iteration
  ...T.jpg|400px|thumb|Fig.1. Iterates of \(T(z)=z^2~\): \(~y\!=\!T^n(x)\!=\!x^{2^n}~\) for various \(n\)]] [[File:FacIteT.jpg|400px|thumb|Fig.2. Iterates of [[Factorial]]: \(~y\!=\!\mathrm{Factorial~}^{~n}(x)~\) for va
  14 KB (2,203 words) - 06:36, 20 July 2020
• Квадратный корень из факториала
  [[File:SquareRootOfFactorial.png|400px|right|thumb| \(y\!=\! x!\) и \(y\!=\!\sqrt{!\,}(x)\) как функции от \(x\)]] ...из факториала ([[Square root of factorial]]), то есть \(\sqrt{\,!\,}\) - голоморфная функкция \(f\) такая, что
  6 KB (312 words) - 18:33, 30 July 2019
• Корень из факториала
  Символ \(\sqrt{\,!\,}\) установлен в качестве эмблемы Физфа
  7 KB (381 words) - 18:38, 30 July 2019
• Filog.cin
  // [[Fixed point]] of [[logarithm]] to base \(\exp(z)\) is evaluated with routine complex double Filog(complex double z 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);
  2 KB (258 words) - 10:19, 20 July 2020
• Filog
  ...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
• ArcSinc
  : \( \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
• Bessel function
  \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) 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
• F45E.cin
  ...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
• F45L.cin
  ...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
• Schroeder equation
  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
• Zooming equation
  (2) \(~ ~ ~ g\big(T(z)\big)= K \, g(z) \) http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html
  10 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

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