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  • 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
  • ...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
  • ...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''' 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
  • are directed to the left hand side of the complex plane, parallel to the real axis. In [[TORI]], this is default choice of th This section describe the [[complex double]] numerical implementation of AuTra. For \(M=9\), the figure at rig
    6 KB (1,009 words) - 18:48, 30 July 2019
  • Article [[Maps of tetration]] collects some [[complex map]]s of [[tetration]] \(\mathrm{tet}_b\) to different values of base \(b\ At the complex maps, the following cases are represented:
    5 KB (761 words) - 12:00, 21 July 2020
  • The [[complex map]]s of them are shown below with levels of constant real part and levels In the most of the complex plane, values of functions
    3 KB (470 words) - 18:47, 30 July 2019
  • be the space of complex-valued functions, including the necessary generalized functions, complex conjugation for ordinary functions and commutes with differentiation.<br>
    38 KB (6,232 words) - 18:46, 30 July 2019
  • ...ve can be used for non-integer \(n\). The exponential can be iterated even complex number of times. ...ion [[tet]] and [[ate]] defines the \(n\)th iterate of exponential for any complex number \(n\) of iterations.
    7 KB (1,161 words) - 18:43, 30 July 2019
  • [[Complex map]]: truncated Taylor expansion of abelsine [[AuSin]], Fig.22.2</p></cent At the front cover, the [[complex map]] of [[natural tetration]] is shown.
    15 KB (2,166 words) - 20:33, 16 July 2023
  • [[File:Moriaamap1.jpg|300px|thumb|Overlaping of the two maps above]] [[Complex map]] of function [[mori]] is shown in the top figure with
    3 KB (456 words) - 18:44, 30 July 2019
  • ...mplex double]] routine in [[C++]] for evaluation of function [[ArcSin]] of complex argument. ...ome reason, the compiler recognises [[exp]], [[log]], [[sin]], [[cos]], of complex argument, but fails with asin and acos.
    4 KB (488 words) - 06:58, 1 December 2018
  • ==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
  • For \(q\!=\!0\), \(q\!=\!1\) and \(q\!=\!2\), [[complex map]] of function \(\mathrm{AuNem}_q\) is shown in figures 2,3,4. ==Extension to the whole complex plane==
    9 KB (1,441 words) - 18:45, 30 July 2019
  • [[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
  • ...n, 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
  • [[Complex map]] of \(\mathrm{Nem}_q\) is shown in figure 2 for \(q\!=\!0\) and in fig ...ive real parameter. Then, Nemtsov Function \(\mathrm{Nem}\) is defined for complex argument \(z\) as follows:
    14 KB (2,157 words) - 18:44, 30 July 2019
  • For \(q\!=\!0.5\), \(q\!=\!1\) and \(q\!=\!2\), the complex maps of function \(\mathrm{StraR}_q\) are shown in figures 2,3,4: Then, evaluation of \(\mathrm{StraRo}_q(z)\) for complex \(z\) can be performed with the short code below:
    4 KB (646 words) - 18:47, 30 July 2019
  • [[Complex map]] of \(~f=\mathrm{SuSin}(x\!+\!\mathrm i y)~ ~\) is shown at right with ...ro; the cut line along the negative part of the real axis is marked at the complex map. Then,
    15 KB (2,314 words) - 18:48, 30 July 2019
  • ...the island of Katav, there is a university and a campus - an architectural complex resembling a cluster of frozen bubbles of a mud geyser (the analogy is corr ...sius, so that the balcony is the second living-room). The "REF-Nido Cereb" complex is financed by one of the largest mega-state public investment funds "Hawai
    367 KB (65,743 words) - 15:48, 1 February 2019
  • The Superfunction, Abelfunction and iterates \(\mathrm{Nem}_q^n\) for complex \(n\) are constructed. G. Szekeres. Regular iteration of real and complex functions. Acta Mathematica, September 1958, Volume 100, Issue 3, pp 203-25
    15 KB (2,392 words) - 11:05, 20 July 2020
  • BRIAN LEHMANN AND JIAN XIAO. CORRESPONDENCES BETWEEN CONVEX GEOMETRY AND COMPLEX GEOMETRY. (2019) [[Complex map]]
    12 KB (1,732 words) - 14:01, 12 August 2020
  • ==[[Complex map]]== In TORI, the [[complex map]]s are used to illustrate [[holomorphic function]]s.
    2 KB (222 words) - 16:00, 28 May 2021
  • ...f the [[Lenin]] monuments and/or Lenin streets (the examples are shown in maps at right). ...Frunse]] and [[Калинин Михаил Иванович|Kalinin]] (see maps at right)
    25 KB (2,722 words) - 14:40, 22 November 2021