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  • [[Tetration]] (or Tetrational) \({\rm tet}_b\) to base \(b \in \mathbb R\), \(b\!>1\)<br> ...\(b\!>\!1\), is holomorphic at least in \(\{ z \in \mathbb C : \Re(z)\!>\!-2\}\).
    21 KB (3,175 words) - 23:37, 2 May 2021
  • http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
    14 KB (2,275 words) - 18:25, 30 July 2019
  • [[Image:Sqrt(factorial)LOGOintegralLOGO.jpg|200px]]<small> [[File:QexpMapT400.jpg|200px]]<br><small><center> \(u+\mathrm i v=\sqrt{\exp} (x+\mathrm i y)\)</center></small>
    25 KB (3,622 words) - 08:35, 3 May 2021
  • 2. <i>Постепенное изменение генотипа из 48 хр ...ец. Заседание Президиума. 'Наука Урала' No. 2 (830), январь 2003.
    111 KB (2,581 words) - 16:54, 17 June 2020
  • ...le:SquareRootOfFactorial.png|400px|right|thumb| \(y\!=\! x!\) and \(y\!=\!\sqrt{!\,}(x)\) verus \(x\)]] [[Square root of factorial]] (half-iteration of [[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\).
    13 KB (1,766 words) - 18:43, 30 July 2019
  • n/2 , \mathrm{ ~~if~~ } n/2 \in \mathbb N \\ (3n\!+\!1)/2 ~ \mathrm{~~over-vice}
    5 KB (798 words) - 18:25, 30 July 2019
  • http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
    20 KB (3,010 words) - 18:11, 11 June 2022
  • ..." is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. The smallest integer larger than 2 (id est 3) is chosen as its value at zero, \(\mathrm{SuperFactorial}(0)=3~\
    18 KB (2,278 words) - 00:03, 29 February 2024
  • : \(T^2(z)=T(T(z))\) ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-175
    4 KB (547 words) - 23:16, 24 August 2020
  • http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html<br> ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
    11 KB (1,644 words) - 06:33, 20 July 2020
  • ...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
  • // 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
  • : \(\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \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
  • : \( \displaystyle \!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \mathrm{Doya}(z)= \mathrm{Tania}\!\Big(1+\mathrm{ArcTania}(z)\Big)\) :\(t\!=\!2\), id est, \(~\mathrm{Doya}^2(x)=\mathrm{Doya}\big(\mathrm{Doya}(x)\big)\)
    19 KB (2,778 words) - 10:05, 1 May 2021
  • : \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \) | \(\displaystyle \frac{-a^2}{z}\)
    11 KB (1,565 words) - 18:26, 30 July 2019
  • [[Square root of exponential]] \(\varphi=\sqrt{\exp}=\exp^{1/2}\) 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
  • ...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
  • [[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
  • Символ \(\sqrt{\,!\,}\) установлен в качестве эмблемы Физфа
    7 KB (381 words) - 18:38, 30 July 2019
  • // [[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

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