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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
  such that, at least for \(b\!>\!1\), is holomorphic at least in \(\{ z \in \mathbb C : \Re(z)\!>\!-2\}\). H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (
  21 KB (3,175 words) - 23:37, 2 May 2021
• Mapping
  ...Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2011)</ref> is holomorphic solution \(F(z)={\rm tet}_b(z)\) of the equations ...map of this function may be interpreted as a hint that the tetrational is holomorphic not only being considered as function of \(z\) at fixed \(b\), but also as
  14 KB (2,275 words) - 18:25, 30 July 2019
• 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
• Natural pentation
  [[File:Penplot.jpg|300px|thumb|\(y=\mathrm{pen}(x)\) and related functions.]] ...[hexation]]. The fixed points of pentation are complex, so, for the real–holomorphic superpentation, the method of the [[Cauchi integral]] can be applied, the s
  7 KB (1,090 words) - 18:49, 30 July 2019
• Square root of factorial
  It is assumed, that \(h\) is [[holomorphic function]] al least in some vicinity of [[halfline]] along the [[real axis] ...y, even the non-integer (and even complex) [[iteration]] of almost every [[holomorphic function]].
  13 KB (1,766 words) - 18:43, 30 July 2019
• Holomorphic extension of the Collatz subsequence
  The holomorphic extension of \(h\) is suggested. The holomorphic extension \(F\) of the sequence, generated with such a transfer function, i
  5 KB (798 words) - 18:25, 30 July 2019
• Regular Iteration
  ...rate''' refer to the [[fractional iterate]] a holomorphic function that is holomorphic in vicinity it its fixed point </ref>. In general, a holomorphic function may have several fixed points, and the fractional iterates, regula
  20 KB (3,010 words) - 18:11, 11 June 2022
• SuperFactorial
  That publication defined the \(\sqrt{!\,}\) as holomorphic function, ...roduct, the [[SuperFunction]] of Factorial and that for some other special functions are considered there.
  18 KB (2,278 words) - 00:03, 29 February 2024
• Transfer equation
  '''Transfer equation''' is relation between some [[holomorphic function]] \(h\), called [[transfer function]] and another function \(F\), ...vial. This determined the interest to the superfunctions from the set of [[holomorphic function]]s of [[complex variable]].
  3 KB (519 words) - 18:27, 30 July 2019
• 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
• Logarithm
  '''Logarithm''' is [[holomorphic function]], inverse of the [[exponential]]. [[Category:Elementary functions]]
  4 KB (661 words) - 10:12, 20 July 2020
• ArcTetration
  H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. [[Aequationes Mathematicae]], v.81, p.65- Abstract — The holomorphic function h is constructed such that h(h(z))=z! ; this function is interpret
  7 KB (1,091 words) - 23:03, 30 November 2019
• Fixed point
  In the simple case, \(f\) is just [[holomorphic function]] of a single variable; then \(L\) is assumed to be a [[complex nu ...] offers the table of evaluations of some fixed points for some elementary functions
  4 KB (574 words) - 18:26, 30 July 2019
• Complex map
  '''Complex map''' is the graphical representation of a [[holomorphic function]] with the isolines of its real part and those of its imaginary pa For any holomorphic function, in any point, the isolines of the real part are orthogonal to tho
  2 KB (254 words) - 06:59, 1 December 2018
• Fslog.cin
  [[Category:Holomorphic functions]]
  5 KB (275 words) - 07:00, 1 December 2018
• Holomorphic function
  '''Holomorphic function''' is concept of the theory of functions of complex variables that refers the the existence of the derivative. Then, function \(f\) is called holomorphic on \(C\).
  1 KB (151 words) - 21:08, 25 January 2021
• Yulya function
  ...proximations for the inverse function, it may have sense to consider it as holomorphic function of the complex argument. [[Category:Mathematical functions]]
  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== '''LambertW''' is [[Holomorphic function]] at the whole complex plane except half-line along the negative p
  8 KB (1,107 words) - 18:26, 30 July 2019

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