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• Factorial
  In [[mathematics]], the '''factorial''' is the [[meromorphic function]] with fast growth along the real axis; fo Frequently, the [[postfix]] notation <math>n!</math> is used for the factorial of number <math>n</math>.
  27 KB (3,925 words) - 18:26, 30 July 2019
• Mapping
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, ...orialQexp.jpg|400px|right|thumb|Complex maps of functions [[square root of factorial]], left, and \(\sqrt{\exp}\), right.]]
  14 KB (2,275 words) - 18:25, 30 July 2019
• Superfunction
  [[Image:Sqrt(factorial)LOGOintegralLOGO.jpg|200px]]<small> [[Superfunction]]s and their inverse functions ([[Abel function]]s) allow evaluation of not only minus-first power of a function (
  25 KB (3,622 words) - 08:35, 3 May 2021
• Square root of factorial
  [[Square root of factorial]] (half-iteration of [[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\). ...some vicinity of [[halfline]] along the [[real axis]], \(h\circ h=\mathrm{Factorial}\). It is assumed that \(z\!=\!2\) is [[regular point]] of \(\sqrt{!\,}(z)
  13 KB (1,766 words) - 18:43, 30 July 2019
• Abel theorem
  In 1824, [[Niels Henrik Abel]] proved the theorem: http://www.cds.caltech.edu/~nair/abel.pdf
  2 KB (320 words) - 18:25, 30 July 2019
• Regular Iteration
  ...al iterate]] of any function $~T~$ through its [[Superfunction]] and the [[Abel function]] is considered as principal, as it allows to deal with functions </ref>, the superfunction of [[factorial]]
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  '''SuperFactorial''', or "superfactorial" is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. : \(\mathrm{SuperFactorial}(z)=\mathrm{Factorial}^z(3)\)
  18 KB (2,278 words) - 00:03, 29 February 2024
• Transfer equation
  ==Abel function and Abel equation== .... Within some domain \(D\in \mathbb C\), the Abel function satisfies the [[Abel equation]]
  3 KB (519 words) - 18:27, 30 July 2019
• Abel function
  For some given [[Transfer function]] \(T\), the '''Abel function''' \(G\) is [[inverse function]] of the corresponding [[superfunct The [[Abel equation]] relates the [[Abel function]] \(G\) and the [[transfer function]] \(T\):
  4 KB (547 words) - 23:16, 24 August 2020
• Transfer function
  In [[TORI]], the term usually refers to the [[Transfer equation]], the [[Abel equation]]; the transfer function is assumed to be given function that appe ...nal restrictions should be applied to make the [[superfunction]] and the [[Abel function]] unique
  11 KB (1,644 words) - 06:33, 20 July 2020
• Nest
  ...ction \(f\) can be expressed through the [[superfunction]] \(F\) and the [[Abel function]] \(G=F^{-1}\): The [[square root of factorial]], that is used as [logo]] of the Physics department of the Moscow State Un
  3 KB (438 words) - 18:25, 30 July 2019
• ArcTetration
  [[ArcTetration]] is [[Abel function]] of the [[exponential]]. The ArcTetration satisfies the [[Abel equation]]
  7 KB (1,091 words) - 23:03, 30 November 2019
• Mathematica
  ...mentations for [[tetration]], [[ArcTetration]], [[SuperFactorial]], [[Abel Factorial]], etc.; of order of a dozen coefficients of the asymptotic expansion can b
  12 KB (1,901 words) - 18:43, 30 July 2019
• Doya function
  ...on]], the [[ArcTania]] function is the [[Abel function]], satisfying the [[Abel equation]] ...09supefae.pdf D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12.
  19 KB (2,778 words) - 10:05, 1 May 2021
• Table of superfunctions
  ...1}\) is called [[Abel function]] with respect to \(T\); it satisfies the [[Abel equation]] function \(G\) can be declared as [[Abel function]], and then the corresponding [[transfer function]]
  11 KB (1,565 words) - 18:26, 30 July 2019
• Square root of exponential
  ...function \(T\) through its [[superfunction]] \(F\) and the corresponding [[Abel function]] \(G=F^{-1}\): ...rfunction]] and the [[Abel function]], and similarly, the [[square root of factorial]]
  5 KB (750 words) - 18:25, 30 July 2019
• Iteration
  ...FacIteT.jpg|400px|thumb|Fig.2. Iterates of [[Factorial]]: \(~y\!=\!\mathrm{Factorial~}^{~n}(x)~\) for various \(n\)]] <ref name="factorial">
  14 KB (2,203 words) - 06:36, 20 July 2020
• Natural tetration
  ...for tetrations to other values of baze and for other funcitons, including factorial and polunomials. \( p\!+\!\mathrm i q=\varphi(z) \) <ref name="factorial">
  14 KB (1,972 words) - 02:22, 27 June 2020
• Квадратный корень из факториала
  : \(\sqrt{\,!\,}(х)=\mathrm{Factorial}^{1/2}(x)\)
  6 KB (312 words) - 18:33, 30 July 2019
• Корень из факториала
  Корень из факториала ([[square root of factorial]]) – это такая функция \(h\), что ...xt.pdf?page=1 D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12
  7 KB (381 words) - 18:38, 30 July 2019

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