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• Factorial
  :<math> F(z+1)=(z+1) F(z) </math> for all complex <math>z</math> except negative integer values.
  27 KB (3,925 words) - 18:26, 30 July 2019
• Tetration
  [[File:Ackerplot.jpg|360px]] : \({\rm tet}_b(z\!+\!1) = \exp_b\!\big( {\rm tet}_b(z) \big)\)
  21 KB (3,175 words) - 23:37, 2 May 2021
• Tetre2215.cc
  // that is convetred to tetreal2215.jpg <br> // Plot of tetrational \(f={\rm tet}_b(z)\)<br>
  6 KB (1,030 words) - 18:48, 30 July 2019
• Mapping
  [[File:Tetreal2215.jpg|300px|right|thumb|Map of function \(f={\rm tet}_b(x)\) in the \(x,b\) plane ...tsov, 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
• Superfunction
  \(\displaystyle {{F(z)} \atop \,} {= \atop \,} {T^z(t) \atop \,} {= \atop \,}
  25 KB (3,622 words) - 08:35, 3 May 2021
• Место науки в человеческом знании
  [[File:DimaY2O3ethanol.jpg|260px]] <!--<small> [[File:Ausinmap52r5.jpg|260px]]<small> <!--
  111 KB (2,581 words) - 16:54, 17 June 2020
• Logiu.cin
  // \(T(z)=4 z (1\!-\!z)\) z_type J(z_type z){ return .5-sqrt(.25-z/Q); }
  3 KB (513 words) - 18:48, 30 July 2019
• Square root of factorial
  ...le:SquareRootOfFactorial.png|400px|right|thumb| \(y\!=\! x!\) and \(y\!=\!\sqrt{!\,}(x)\) verus \(x\)]] ...[[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\).
  13 KB (1,766 words) - 18:43, 30 July 2019
• Holomorphic extension of the Collatz subsequence
  : \(h(F(z))=F(z\!+\!1)\) [[File:File-Sirakuse03a.jpg|right|500px|thumb|Complex map of function \(F\)]]
  5 KB (798 words) - 18:25, 30 July 2019
• Regular Iteration
  ...tsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756. :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z\!+\!1)=T(F(z))$
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  : \(\mathrm{SuperFactorial}(z)=\mathrm{Factorial}^z(3)\) : \(\mathrm{Factorial}(\mathrm{SuperFactorial}(z))=\mathrm{SuperFactorial}(z\!+\!1)\)
  18 KB (2,278 words) - 00:03, 29 February 2024
• Transfer function
  D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. ...tsov, 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
• Nest
  :\(\mathrm{Nest}[f,z,c]\) where \(f\) is name of iterated function, \(z\) is initial value of the argument, and \(c\) is number of iterations.
  3 KB (438 words) - 18:25, 30 July 2019
• Japan
  [[File:Japan2459014.6416.jpg|320px|right]] [[File:MicroChipAtomicTrap00.jpg|144px]] <small>[[microchip atom trap|Atom trap]] <ref name="nakagawa2006">{
  15 KB (2,106 words) - 13:37, 5 December 2020
• ArcTetration
  D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation 78 (2009), 1647-1670. : \( \mathrm{ate}_b(\mathrm{tet}_b(z))=z \)
  7 KB (1,091 words) - 23:03, 30 November 2019
• Tania function
  f'(z)= \frac{f(z)}{1+f(z)} ...nd then along the straight line (parallel to the real axis) to the point \(z\).
  27 KB (4,071 words) - 18:29, 16 July 2020
• Doya function
  In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be expressed through the \mathrm{Doya}(z)=\mathrm{LambertW}\Big( z~ \mathrm{e}^{z+1} \Big)\)
  19 KB (2,778 words) - 10:05, 1 May 2021
• Doya.cin
  z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
  3 KB (480 words) - 14:33, 20 June 2013
• Table of superfunctions
  : \( \!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z+1)=T(F(z)) \) : \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \)
  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 tha : \(\!\!\!\!\!\!\!\!\!\!\!\!\!(1) ~ ~ ~ \varphi(\varphi(z))=z\)
  5 KB (750 words) - 18:25, 30 July 2019

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