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• Serega function
  The Serega function is not holomorphic, and, therefore, not differentiable, id est, the derivative depends on the are derivatives of functions \(X\) and \(Y\) with respect to the last argument.
  5 KB (674 words) - 18:25, 30 July 2019
• LogisticSequence
  ...article [[Logistic sequence]] and links cited there, in particular, the [[Holomorphic extension of the logistic sequence]]. ...quence and its inverse functions can be expressed in terms of [[elementary functions]],
  7 KB (886 words) - 18:26, 30 July 2019
• ArcLogisticSequence
  [[ArcLogisticSequence]]\(_s\) is holomorphic function, inverse of function [[LogisticSequence]], ...is usually interpreted as operation of multiplication or [[combination of functions]].
  3 KB (380 words) - 18:25, 30 July 2019
• Logistic operator
  D.Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, 201 Many superfuncitons for the given transfer function exist; and many Abel functions exist too. That called ArcLogisticSequance seems to be the simplest one. Ac
  6 KB (817 words) - 19:54, 5 August 2020
• WrightOmega
  [[WrightOmega]] is holomorphic function, solution \(f\) of equations For this reason, both functions, [[Tania function]] and [[WrightOmega]] are used in [[TORI]].
  4 KB (610 words) - 10:22, 20 July 2020
• Keller function
  In the strip \(|\Im(z)|<\pi\), functions Keller and Keller\(_0\) are equivalent, \(\mathrm{Keller}(z)=\mathrm{Keller ...sidered also as just a complex variable; so, the Keller is treated as just holomorphic function of complex argument.
  10 KB (1,479 words) - 05:27, 16 December 2019
• Shoko function
  ...ty of the real axis (and, in particular, for real values of the argument), functions [[Shoka function|Shoka]] and [[Shoko function|Shoko]] coincide. The [[Shoko function]] can be expressed through the elementary functions:
  10 KB (1,507 words) - 18:25, 30 July 2019
• AuZex
  The should be unique, in order to avoid confusion with other functions, while all figures are collected in the same directory for some article or two different functions are used in the same expression.<br>
  6 KB (899 words) - 18:44, 30 July 2019
• Name of function
  ...in order to distinguish it/him/her from other element of the same set. For functions, the name is especially important because it allows to denote the complicat Usually, the names of functions use the ascii characters, namely, letters and, in exceptional cases, [[cife
  6 KB (901 words) - 18:27, 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
  ...t it is entire elementary function. The Trappmann function is example of [[holomorphic function]] without [[fixed point]]s, suggested in year 2011 by [[Henryk Tra ...</ref>, it is possible to construct at least one [[superfunction]] for any holomorphic function. Therefore, the consideration of the Trappmann function as [[trans
  9 KB (1,320 words) - 11:38, 20 July 2020
• C++
  In order to follow the descriptions of functions and to reproduce and to modify the figures suggested, the installing of C++ ...enerates the [[contour plot]]s; and in particular, the [[complex map]]s of functions of compex variables
  4 KB (608 words) - 15:01, 20 June 2013
• Schroeder equation
  Usially, it is assumed that \(s\!=\!T'(0)\), and both, \(T\) and \(g\) are holomorphic at least in some vicinity of zero. </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. For a given function \(~T~\), [[holomorphic function|holomorphic]] in vicinity of its [[fixed point]] \(~L~\), the function
  2 KB (272 words) - 18:25, 30 July 2019
• Zooming equation
  ...d that \(K\) is positive real number, id est, \(K>0\), and \(T\) is real–holomorphic, G. Szekeres. Regular iteration of real and complex functions.
  10 KB (1,627 words) - 18:26, 30 July 2019
• AuTra
  [[AuTra]] is real-holomorphic, \(\mathrm{AuTra}(z^*)=\mathrm{AuTra}(z)^*\) ...uired to plot the camera-ready pictures of the complex maps of the related functions.
  6 KB (1,009 words) - 18:48, 30 July 2019

• File:AcosqplotT100.png [[ArcCosc]], [[ArcCosq]], [[Sazae-san functions]], [[Category:Holomorphic function]] (2,231 × 1,215 (152 KB)) - 09:41, 21 June 2013

• File:ArcSeregaMapT.png Neither [[Serega function]] nor [[ArcSerega]] are [[holomorphic]]; the asterisk in the definition above denotes the [[complex conjugation]] // WARNING: non-holomorphic functions included! (1,312 × 1,312 (483 KB)) - 09:43, 21 June 2013

• File:B271a.png The ArcTetration $\mathrm{ate}$ is inverse of [[tetration]] and holomorphic solution of the [[Abel equation]] H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 ( (1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018

• File:E1efig09abc1a150.png [[Category:Holomorphic functions]] (2,234 × 711 (883 KB)) - 08:34, 1 December 2018

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