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• Factorial
  ....Stegun: Handbook of Mathematical Functions. 6. Gamma Function and Related Functions (2010) ...r <math>z</math>, the integral can be expressed in terms of the elementary functions.
  27 KB (3,925 words) - 18:26, 30 July 2019
• Tetration
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( ...e requirements of the [[computational mathematics]] in the rapidly growing functions; if not, the superfunction of tetration, id est, [[pentation]] (\(\mathrm {
  21 KB (3,175 words) - 23:37, 2 May 2021
• Superfunction
  In particular, the [[Ackernann functions]] and [[tetration]] can be interpreted in terms of [[superfunction]]s. ...ns came from the application to the evaluation of fractional iterations of functions.
  25 KB (3,622 words) - 08:35, 3 May 2021
• Square root of factorial
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (
  13 KB (1,766 words) - 18:43, 30 July 2019
• Holomorphic extension of the Collatz subsequence
  In the similar way, the inverse of the Collatz sequence can be generalized. [[Category:Mathematical functions]]
  5 KB (798 words) - 18:25, 30 July 2019
• Regular Iteration
  ...he [[Abel function]] is considered as principal, as it allows to deal with functions that have no real fixed points (and, perhaps, no fixed points at all). </ref>) and its inverse function.
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  ...roduct, the [[SuperFunction]] of Factorial and that for some other special functions are considered there. The inverse function of SuperFactorial is [[AbelFactorial]]; at least in some vicinity
  18 KB (2,278 words) - 00:03, 29 February 2024
• Transfer equation
  The Inverse of the Superfunction, \(G=F^{-1}\) is called [[Abel function]]. Within some In particular, \(h^{-1}\) is the inverse function, \(h^0\) is the [[identity function]] and \(h^1=h\).
  3 KB (519 words) - 18:27, 30 July 2019
• Abel function
  ...some given [[Transfer function]] \(T\), the '''Abel function''' \(G\) is [[inverse function]] of the corresponding [[superfunction]] \(F\), id est, \(G=F^{-1} : \(T^{-1}\) is inverse function of \(T\)
  4 KB (547 words) - 23:16, 24 August 2020
• Transfer function
  [[File:KellerDoyaT.png|300px|thumb|Transfer functions of laser amplifiers with simple kinetics for the short pulses ([[Keller fun H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (
  11 KB (1,644 words) - 06:33, 20 July 2020
• Abel equation
  The [[Abel function]] \(G\) is considered as inverse of the [[superfunction]] \(F\). ...no need to be integer. For the case of integer iterations, \(T^{-1}\) is inverse function of \(T~, ~ ~\)
  4 KB (598 words) - 18:26, 30 July 2019
• Logarithm
  '''Logarithm''' is [[holomorphic function]], inverse of the [[exponential]]. For arbitrary base \(b\), the function \(\log_b\) is [[inverse function]] of the exponential to base \(b\);, id est, \(\exp_b\);
  4 KB (661 words) - 10:12, 20 July 2020
• Biogenesis
  ...life at the Earth. If one suppose the finite age of the Universe (roughly, inverse of the [[Hubble constant]]), then the life had to be created as some stage The concept about finite [[age of our Universe]] (roughly expressed with the inverse of the [[Hubble constant]]) implies that the life was somehow created, alth
  16 KB (2,012 words) - 01:09, 31 December 2018
• ArcTetration
  [[ArcTetration]] \( \mathrm{ate} \) is inverse function of [[tetration]] Being the inverse function of [[tetration]], the ArcTetration \( \mathrm {ate}_b \) to base \
  7 KB (1,091 words) - 23:03, 30 November 2019
• Fixed point
  In some cases, the [[inverse function]] \(g=f^{-1}\) exists, and often the fixed point of function \(f\) ...] offers the table of evaluations of some fixed points for some elementary functions
  4 KB (574 words) - 18:26, 30 July 2019
• Yulya function
  The '''ArcYulya function''' is just inverse function of Yulya, id est, \(\mathrm{ArcYulya}_a=\mathrm{Yulya}_a^{-1}\) in ...properties Yulya and the building up the efficient approximations for the inverse function, it may have sense to consider it as holomorphic function of the c
  12 KB (1,754 words) - 18:25, 30 July 2019
• Tania function
  ==Relation to other special functions== According to the Axiom [[TORI]] number 6, the simplest among related functions should be considered as principal, primary. From this axiom, it follows, th
  27 KB (4,071 words) - 18:29, 16 July 2020
• LambertW function
  ==Relation with other functions== the inverse function of [[ArcLambertW]]. In [[TORI]], ArcLambertW is denoted also as [[
  8 KB (1,107 words) - 18:26, 30 July 2019
• Doya function
  ...[Doya function]] can be defined in terms of the [[Tania function]] and its inverse function with equation and ArcTania function is its inverse function, it can be expressed as
  19 KB (2,778 words) - 10:05, 1 May 2021
• Fourier transform
  The inverse of Fourier operator is also its Hermitian–conjugated, id est, For the integrable continuous functions \(A\) and \(B\), it is assumed that
  11 KB (1,501 words) - 18:44, 30 July 2019

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