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• Doya function
  ...ng with real numbers. However, the difference become clearly seen is these functions are plotted in the complex plane. ...ermined by the two parameters \(P_{\rm sat}\) and \(t\) through the known functions Doya and Tania. Such a model seems to be applied, in particular, for the [[
  19 KB (2,778 words) - 10:05, 1 May 2021
• Table of superfunctions
  For a given function \(T\), called [[transfer function]], the holomorphic solution \(F\) of [[Transfer equation]] In any pair of holomorphic functions \(F\), \(G\!=\!F^{-1}\),
  11 KB (1,565 words) - 18:26, 30 July 2019
• Square root of exponential
  Such a \(\varphi\) is assumed to be [[holomorphic function]] for some domain of values of \(z\). </ref> in the middle or 20 century. But the [[real-holomorphic]] solution was not constructed that time.
  5 KB (750 words) - 18:25, 30 July 2019
• 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
  For example, the existence and uniqueness of the holomorphic [[tetration]] with certain properties is declared as theorem in the first p 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
  Function \(\mathrm {tet}(z)\) is holomorphic in the whole complex plane except the line \(\Re(z)\le -2\). where \(\eta\) is holomorphic periodic function with period unity,
  14 KB (1,972 words) - 02:22, 27 June 2020
• Квадратный корень из факториала
  http://www.springerlink.com/content/u712vtp4122544x4 D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201 ...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 (
  6 KB (312 words) - 18:33, 30 July 2019
• Iterated integral
  ...rithm, the \(J^n f\) may have singularities and cutlines even if \(f\) is holomorphic function. ...ay consider application of the fractional differentiation to some specific functions; for example, the polynomial or the exponential.
  9 KB (1,321 words) - 18:26, 30 July 2019
• Корень из факториала
  http://www.springerlink.com/content/u712vtp4122544x4 D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201 ...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 (
  7 KB (381 words) - 18:38, 30 July 2019
• ArcCos
  '''ArcCos''', or '''acos''' is [[holomorphic function]], inverse of [[cos]]. '''ArcCos''', or '''acos''', or '''arccos''' is [[holomorphic function]], inverse of [[cos]].
  5 KB (754 words) - 18:47, 30 July 2019
• ArcCip
  Cih is also real-holomorphic, The notations of this article are not good. Many other similar functions should be described and implemented, anf theu should have similar names. Th
  8 KB (1,211 words) - 18:25, 30 July 2019
• ArcSin
  '''ArcSin''', or '''asign''', or '''arcsin''' is [[holomorphic function]], inverse of [[sin]]; \(f=\arcsin(z)\) is holomorphic solution \(f\) of equation
  9 KB (982 words) - 18:48, 30 July 2019
• Coshc
  Functions \(~y\!=\!\mathrm{coshc}(x)~\) and \(~y\!=\!\mathrm{coshc}'(x)~\) are shown Coshc is [[holomorphic function]] with the only singularity, namely, pole at zero.
  4 KB (509 words) - 18:26, 30 July 2019
• ArcCosc
  Knowledge of these constants simplifies evaluation of functions [[ArcCosc]] and [[ArcCohc]]. ...Cosc]] as it it would be elementary function. It has sense to include such functions as [[Tetration]], [[ArcTetration]], [[SuperFactorial]], [[AbelFactorial]],
  8 KB (1,137 words) - 18:27, 30 July 2019
• ArcCosqq
  '''ArcCosqq''' is holomorphic function defined with through functions [[acosq]] (or [[ArcCosq]]) expressed with
  2 KB (216 words) - 18:26, 30 July 2019
• Acosc1
  '''Acosc1''' is the holomorphic continuation of function [[ArcCosc]] behind the cut line along the negative Acosc1 is [[real holomorphic function]]; for all the branches numbered in this way, the relation below h
  6 KB (896 words) - 18:26, 30 July 2019
• BesselJ0
  The BesselJ0 is real-holomorphic, Along the real axis, BesselJ0 oscillates (like other [[Bessel]] functions). The zeros of are denoted with \(j_{0,n}\); where \(n\) is supposed to be
  6 KB (913 words) - 18:25, 30 July 2019
• BesselK0
  '''BesselK0''' or \(K_0\) is holomorphic function, solution \(f\) of equation
  3 KB (394 words) - 18:26, 30 July 2019
• Ocean wave solution
  The only functions can be differentiated, and the name of this function should be explicitly d The [[Serega function]] is not holomorphic; to, the separate expressions for the real and imaginary parts are used. Th
  12 KB (1,879 words) - 18:26, 30 July 2019
• Serega.cin
  // '''serega.cin''' is the numerical [[C++]] implementation of functions // Warining: non-holomorphic functions below!
  1 KB (265 words) - 15:00, 20 June 2013

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