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• Factorial
  For complex values of the argument, the combinatoric definition above should be extende for all complex <math>z</math> except negative integer values.
  27 KB (3,925 words) - 18:26, 30 July 2019
• Tetration
  ...d that \({\rm tet}_b(z^*)={\rm tet}_b(z)^*\), where the asterisk means the complex conjugation. For the case of base \(b \!=\! \mathrm e\), the index may be o Case of complex values of \(b\) is under investigation; conditions, that make the solution
  21 KB (3,175 words) - 23:37, 2 May 2021
• Mapping
  ...lactic meridian]] at the sky sphere. Similarly, the geophysicists use some maps without to know what kind of function (it is called "projection") relates t ...home.html D.Kouznetsov. (2009). Solutions of \(F(z+1)=\exp(F(z))\) in the complex plane.. Mathematics of Computation, 78: 1647-1670. DOI:10.1090/S0025-5718-0
  14 KB (2,275 words) - 18:25, 30 July 2019
• Superfunction
  ...s-first power of a function (inverse function), but also any real and even complex [[iteration]] of the function. The [[complex map]]s of functions \( \sqrt{\exp} \) and \(\sqrt{!} \) are shown in figur
  25 KB (3,622 words) - 08:35, 3 May 2021
• Regular Iteration
  ...xed point]] of the transfer function) either in the right hand side of the complex plane, or in the left hand side. In the opposite direction, the superfuncti For [[real-holomorphic]] transfer function, the the [[complex map]] of such superfunction reproduces itself at the translations for $2\pi
  20 KB (3,010 words) - 18:11, 11 June 2022
• Complex map
  '''Complex map''' is the graphical representation of a [[holomorphic function]] with t ...t are orthogonal to those of the imaginary part; therefore the the complex maps have specific mesh-like structure.
  2 KB (254 words) - 06:59, 1 December 2018
• B271az.cc
  // showing the [[complex map]] of [[ArcTetration]] to base e. #include<complex>
  3 KB (529 words) - 14:32, 20 June 2013
• B271a.tex
  % which is [[complex map]] of function [[ate]] %<br> % [[Category:Complex maps]]
  2 KB (303 words) - 18:48, 30 July 2019
• Tania function
  However, neither algorithm for the evaluation not complex maps of the WrightOmega are suggested there. The [[complex map]]s of the ArcTania and Tania functions are shown in the figures at righ
  27 KB (4,071 words) - 18:29, 16 July 2020
• Iteration
  ...nctions \(F\) and \(G\) are established, the function can be iterated even complex number of times. D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
  14 KB (2,203 words) - 06:36, 20 July 2020
• Natural tetration
  D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. Function \(\mathrm {tet}(z)\) is holomorphic in the whole complex plane except the line \(\Re(z)\le -2\).
  14 KB (1,972 words) - 02:22, 27 June 2020
• ArcCip
  [[File:CipmapT.png|400px|thumb|[[complex map]] of \(u+\mathrm i v=\mathrm{Cip}(x+\mathrm i y)\)]] [[File:AcipmapTpng.png|400px|thumb|[[complex map]] of \(u+\mathrm i v=\mathrm{ArcCip}(x+\mathrm i y)\)]]
  8 KB (1,211 words) - 18:25, 30 July 2019
• ArcCosc
  [[File:acoscmapT300.png|600px|thumb|[[complex map]] of \(u+\mathrm i v=\mathrm{acosc}(x+\mathrm i y)\)]] ...e, the robust [[C++]] implementation is supplied in the description of the complex map (click on the map at right).
  8 KB (1,137 words) - 18:27, 30 July 2019
• LogisticSequence
  where \(z\) is complex number and \(s\) is real number; usually it is assumed that \(s>1\). ...plots of LogisticSequence are shown in two figures at right. Below, the [[complex map]]s of function \(\mathrm{LogisticSequence}_s\) are shown for \(s\!=\!3\
  7 KB (886 words) - 18:26, 30 July 2019
• Efjh.cin
  ...der to compile the generators of pictures ([[explicit plot]]s and/or the [[complex map]]s) of the [[LogisticSequence]]. Sorry for use of global variables; in
  3 KB (364 words) - 07:00, 1 December 2018
• ArcLogisticSequence
  ...own in figure below. However, with the code supplied, one can plot similar maps for other values of parameter \(s\).
  3 KB (380 words) - 18:25, 30 July 2019
• WrightOmega
  ...f the fixed point of logarithm and used in definition of [[tetration]] for complex base \(b=\log(a)\), can be expressed through the [[WrightOmega]]. </ref>. However, neither the efficient algorithms, nor the complex maps for the [[WrightOmega]] are presented in the descriptions cited; so, at lea
  4 KB (610 words) - 10:22, 20 July 2020
• Shoka function
  [[Complex map]] of the [[Shoka function]] is shown in figure at right. The [[Shoka function]] is holomorphic at the complex plane with cuts
  3 KB (421 words) - 10:23, 20 July 2020
• ArcKeller
  The [[complex map]]s of the [[Keller function]] and the [[ArcKeller]] function are shown
  4 KB (545 words) - 18:26, 30 July 2019
• SuZex approximation
  [[File:SuZexMapT.jpg|600px|thumb|Fig.2.[[Complex map]] of function [[SuZex]]: \(~u\!+\!\mathrm i v= \mathrm{SuZex}(x_1+x\!+\ ...for various approximations of [[SuZex]] with elementary functions. All the maps are supposed to be displayed in the same scale.
  14 KB (2,037 words) - 18:25, 30 July 2019

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