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• Strip asymptotic
  ...vior of a function in an **unbounded horizontal or vertical strip** of the complex plane, rather than in an angular sector. Let \(f\) be a complex-valued function.
  2 KB (319 words) - 18:27, 10 January 2026
• Sectorial asymptotic
  ...ymptotic]] whose [[domain of validity]] is restricted to a [[sector of the complex plane]]. This type of asymptotic is widely used in [[complex analysis]] and in the theory of [[special function]]s, especially for describing the
  3 KB (463 words) - 21:03, 12 January 2026
• Mathematics of Computation
  numerical analysis, computational discrete mathematics, number theory, algebra, combinatorics, D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
  2 KB (344 words) - 07:02, 1 December 2018
• Mandelbrot polynomial
  whrere \(c\) is parameter. Usially, it is assumed to be a [[complex number]]. ...be integer; the [[Mandelbrot polynomial]] can be iterated arbitrary (even complex) number of times.
  2 KB (229 words) - 18:44, 30 July 2019
• Linear fuction
  where \(A\) and \(B\) are constants (for example some complex numbers) ...r. As other holomophic functions, the linear function can be iterated even complex number of times.
  2 KB (234 words) - 18:43, 30 July 2019
• Examples of sectorial and strip asymptotics
  Terms related to [[asymptotic]] behavior of functions of a complex variable caused confusions. The description of [[asymptotic]] analysis at Wikipedia <ref>
  3 KB (411 words) - 18:55, 10 January 2026
• Lof
  ...\big(\)[[Factorial]]\((z)\big)~\) , that is holomorphic in the most of the complex \(z\) plane (except \(z\!\le\!-1\)). [[Complex map]] of function [[lof]] is shown in figure at right with lines \(u\!+\!\m
  3 KB (478 words) - 18:43, 30 July 2019
• Theorem on increment of tetration
  ...009analuxpRepri.pdf D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. [[Mathematics of Computation]], v.78 (2009), 1647-1670. ...-1 [[William Paulsen]] and [[Samuel Cowgill]]. Solving F(z+1)=bF(z) in the complex plane. Advances in Computational Mathematics, 2017 March 7, p. 1–22
  4 KB (548 words) - 14:27, 12 August 2020
• Cosc
  [[File:CoscmapT100.png|800px|right|thumb|[[Complex map]] of [[cosc]], \(u+\mathrm i v = \mathrm{cosc}(x+\mathrm i y)\) ]] ==Complex map of [[cosc]]==
  4 KB (649 words) - 18:26, 30 July 2019
• ArqNem
  ==Complex maps== Complex maps of function \(\mathrm{ArqNem}_q(z)\) is shown in figures at right for
  7 KB (1,319 words) - 18:46, 30 July 2019
• NemBran
  ...[Nemtsov function]] \(\mathrm{Nem}_q\) versus parameter \(q\). While, only analysis for the real \(q\) is presented. For real \(q\) function \(\mathrm{Nem}_q\) ...ns should be implemented in the most of the complex plane, id est, for the complex argument.
  3 KB (400 words) - 18:48, 30 July 2019
• Entire Function with Logarithmic Asymptotic
  However the sector may cover almost all the complex plane, excluding an arbitrary narrow sector along the negative part of the is function \(\Phi\) of complex argument such that
  7 KB (1,073 words) - 12:35, 10 January 2026
• Base e1e
  [[File:Expe1emapT1000.jpg|200px|thumb|[[Complex map|Map]] of \(~f\!=\!\eta\!=\!\exp_{\exp(1/\mathrm e)}~\); here \(~u+\math [[File:Loge1emapT1000.jpg|200px|thumb|[[Complex map|Map]] of \(~f\!=\!\log_{\exp(1/\mathrm e)}~\); here \(~u+\mathrm i v=f(
  4 KB (559 words) - 17:10, 10 August 2020
• Maga
  ...st option, the holomorphic properties of the functions involved (and their complex maps) should be analysed. ...tation indicates the way of holomorphic extension of function [[maga]] for complex values of the argument \(z\); the appropriate paths of integration should b
  8 KB (1,256 words) - 18:44, 30 July 2019
• Serega function
  '''Serega function''' is nongolomorphic function \(\mathrm{Serega}\) of complex variable \(z\) such that where the asterisk means the [[complex conjugation]].
  5 KB (674 words) - 18:25, 30 July 2019
• Iterated integral
  ...ple case of natural \(n\) can be generalized for integer rational and even complex values of \(n\); such a generalization is allows to deal with derivatives of arbitrary (negative, fractal and even complex order.
  9 KB (1,321 words) - 18:26, 30 July 2019
• Ackermann function
  For given complex number \(b\), called "base", and given integer number \(n\), called "number ...this case is easier to interpret and to apply in physics, than cases with complex \(b\).
  10 KB (1,534 words) - 06:44, 20 July 2020
• Amos
  Below the complex map of function [[Amos]] is shown with lines of its content real part and l ...necessary for [[summation of the asymptotic series]], the extension to the complex plane is essential. For this reason, the special name is required for the h
  6 KB (883 words) - 18:44, 30 July 2019
• Shoko function
  For the analysis of the Keller function, another superfunction, namely, [[Shoka function]] h The [[complex map]] of the [[Shoko function]] is shown in figure at right.
  10 KB (1,507 words) - 18:25, 30 July 2019
• Tetre2215.cc
  // The numerical implementation of the complex tet(complex,complex) <br> // but for the serious numerial analysis the number of terms in the expansion should be increased;<br>
  6 KB (1,030 words) - 18:48, 30 July 2019

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