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• For complex values of the argument, the combinatoric definition above should be extende for all complex $z$ except negative integer values.
27 KB (3,925 words) - 18:26, 30 July 2019
• ...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
• ...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
• ...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
• '''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
• // showing the [[complex map]] of [[ArcTetration]] to base e. #include<complex>
3 KB (529 words) - 14:32, 20 June 2013
• % which is [[complex map]] of function [[ate]] %<br> % [[Category:Complex maps]]
2 KB (303 words) - 18:48, 30 July 2019
• 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
• ...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
• 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
• [[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
• [[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
• 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 • ...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 • ...own in figure below. However, with the code supplied, one can plot similar maps for other values of parameter \(s$$.
3 KB (380 words) - 18:25, 30 July 2019
• ...f the fixed point of logarithm and used in definition of [[tetration]] for complex base $$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
• [[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
• The [[complex map]]s of the [[Keller function]] and the [[ArcKeller]] function are shown
4 KB (545 words) - 18:26, 30 July 2019
• [[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
• ...n of the previously developed language '''C''', that allows to deal with [[complex number]]s and has many other advantages. ...ne [[conto.cin]] generates 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

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