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• Iteration
  Walter Bergweiler. Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151-188 For iteration of functions, the same notation is used also by [[Walter Bergweiler]]
  14 KB (2,203 words) - 06:36, 20 July 2020
• Theorem
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (
  2 KB (248 words) - 14:33, 20 June 2013
• Natural tetration
  The pair of functions \(\mathrm {tet}\) and \(\mathrm{ate}\) The non–integer iterations of exponential give the class of functions that grow faster than any polynomial but slower than any exponential.
  14 KB (1,972 words) - 02:22, 27 June 2020
• Квадратный корень из факториала
  ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( [[Category:Mathematical functions]]
  6 KB (312 words) - 18:33, 30 July 2019
• Корень из факториала
  ...t/u7327836m2850246/ H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( [[Category:Abel function]]
  7 KB (381 words) - 18:38, 30 July 2019
• ArcLogisticSequence
  ...is usually interpreted as operation of multiplication or [[combination of functions]]. ArcLogisticSequence is [[Abel function]] for the [[Logistic operator]] as the transfer function,
  3 KB (380 words) - 18:25, 30 July 2019
• Logistic operator
  ...[superfunction]]s is called [[Logistic sequence]], and the corresponding [[Abel function]] is called [[ArcLogisticSequence]]. ==Abel function of the Logistic operator==
  6 KB (817 words) - 19:54, 5 August 2020
• ArcShoka
  [[ArcShoka]] function is inverse function of [[Shoka function]] and [[Abel function]] for the [[Keller function]]; ==Various inverse functions==
  3 KB (441 words) - 18:26, 30 July 2019
• ArcKeller
  ...e [[Keller function]]; there exist the explicit representations for these functions through the [[elementary function]]s: ...[[ArcShoka]] and [[Shoka function]]s, as they are [[superfunction]] and [[Abel function]] of the Keller function:
  4 KB (545 words) - 18:26, 30 July 2019
• ArcLambertW
  ...x]]; \(\mathrm{AuZex}=\mathrm{SuZex}^{-1}\). This function satisfies the [[Abel equation]] With [[superfunction]] of [[zex]], called [[SuZex]], and the [[Abel function]], called [[AuZex]], the [[iterations]] of [[zex]] can be expresse
  3 KB (499 words) - 18:25, 30 July 2019
• AuZex
  [[AuZex]] is also [[Abel function]] for the [[transfer function]] \(\mathrm{zex}(z)=z \exp(z)\). Also, [[AuZex]] satisfies the [[Abel equation]]
  6 KB (899 words) - 18:44, 30 July 2019
• Power function
  These functions can be verified with the Mathematica code below: <poem><nomathjax><nowiki> ...ld be applied to the result. Often this appears dealing with trigonometric functions, one writes, for example, \(\sin^a(z)\) instead of \(\sin(z)^a~\). <!-- How
  15 KB (2,495 words) - 18:43, 30 July 2019
• Trappmann function
  ...ered as a serious obstacle at the building-up its [[superfunction]], the [[Abel function]] and the non–integer [[iterate]]s of function Tra. The inverse function, id est, the [[Abel function]] of \(\mathrm{Tra}\), may be called [[Ahe]] or [[ahe]], in a way
  9 KB (1,320 words) - 11:38, 20 July 2020
• Schroeder equation
  ...[[Schroeder function]]s ) are related to the [[superfunction]]s and the [[Abel function]]s. </ref>; their functions are pretty different.
  8 KB (1,239 words) - 11:32, 20 July 2020
• Fractional iterate
  [[Fractional iterate]] is concept used to construct non-integer iterates of functions. ...ior at infinity, or specification of the [[superfunction]] \(F\) and the [[Abel function]] \(G=F^{-1}\), used to construct the fractional iterate \(T^r\) w
  2 KB (272 words) - 18:25, 30 July 2019
• Zooming equation
  G. Szekeres. Regular iteration of real and complex functions. ...various functions can be constructed also with the [[superfunction]] and [[Abel function]], considering the [[transfer equation]] instead of the [[zooming
  10 KB (1,627 words) - 18:26, 30 July 2019
• SuTra
  ...e function of SuTra, id est, [[AuTra]]\(=\)SuTra\(^{-1}\), satisfies the [[Abel equation]] ...n function is important example of function without [[fixed points]]. Such functions were expected to be difficult for construction of the [[fractional iterate]
  9 KB (1,285 words) - 18:25, 30 July 2019
• ArcTra
  ...ing of approximation of solution of algebraic equation with differentiable functions: The agreement functions for the primary approximations app1, app2, app3, app4 described above and f
  10 KB (1,442 words) - 18:47, 30 July 2019
• AuTra
  [[AuTra]] is [[Abel function]] of the [[Trappmann function]], \(\mathrm{tra}(z)=z+\exp(z)\). [[AuTra]] satisfies the Abel equation
  6 KB (1,009 words) - 18:48, 30 July 2019
• Abelpower
  [[Abelpower]] is [[Abel function]] for the [[power function]], id est, transfer function \(T(z)\!=\ ...] function \(F\), the inverse function \(G\!=\!F^{-1}\) is solution of the Abel equation,
  3 KB (470 words) - 18:47, 30 July 2019

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