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  • Regular Iteration
    :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z\!+\!1)=T(F(z))$ :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \displaystyle F(z) = L+\sum_{n=1}^{N} a_n \varepsilon^n + o(\varepsilon^N)$ , where $\varepsi
    20 KB (3,010 words) - 18:11, 11 June 2022
  • SuperFactorial
    : \(\mathrm{SuperFactorial}(z)=\mathrm{Factorial}^z(3)\) : \(\mathrm{Factorial}(\mathrm{SuperFactorial}(z))=\mathrm{SuperFactorial}(z\!+\!1)\)
    18 KB (2,278 words) - 00:03, 29 February 2024
  • Transfer equation
    : \(F(z\!+\!1)=h(F(z))\) for all \(z\in C \subseteq \mathbb C\).
    3 KB (519 words) - 18:27, 30 July 2019
  • Abel function
    : \(G(T(z))=G(z)+1\) In certain range of values of \(z\), this equation is equivalent of the [[Transfer equation]]
    4 KB (547 words) - 23:16, 24 August 2020
  • Transfer function
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. : \((1) ~ ~ ~ ~ ~ F(z\!+\!1)=h(F(z))\)
    11 KB (1,644 words) - 06:33, 20 July 2020
  • Abel equation
    : \((1)~ ~ ~ ~ ~ G(T(z))=G(z)+1\) at least for \(z\) from some domain in the complex plane.
    4 KB (598 words) - 18:26, 30 July 2019
  • Navier-Stokes equation
    ...}{r} \frac{\partial u_r}{\partial \phi} + u_z \frac{\partial u_r}{\partial z} - \frac{u_{\phi}^2}{r}\right) = ...^2}\frac{\partial^2 u_r}{\partial \phi^2} + \frac{\partial^2 u_r}{\partial z^2}-\frac{u_r}{r^2}-\frac{2}{r^2}\frac{\partial u_\phi}{\partial \phi} \righ
    7 KB (1,149 words) - 18:26, 30 July 2019
  • Logarithm
    :\( \exp(\ln(z))=z ~ ~\) for all from the range of definition; : \(\exp_b(z)=b^z\)
    4 KB (661 words) - 10:12, 20 July 2020
  • Nest
    :\(\mathrm{Nest}[f,z,c]\) where \(f\) is name of iterated function, \(z\) is initial value of the argument, and \(c\) is number of iterations.
    3 KB (438 words) - 18:25, 30 July 2019
  • Japan
    | doi= 10.1007/s00340-005-2083-z | doi= 10.1007/s00340-005-2083-z
    15 KB (2,106 words) - 13:37, 5 December 2020
  • Microchip atom trap
    ...plied Physics B 82 (3): 363–366.(2006). <!-- doi:10.1007/s00340-005-2083-z !--> ...agnet traps, [[Ioffe configuration trap]]s, [[QUIC trap]]s and others. The z-type trap shown in the picture happened to be to easy to manufacture and ef
    9 KB (1,400 words) - 18:26, 30 July 2019
  • Quantum reflection
    ...has translational symmetry in two directions (say <math>y</math> and <math>z</math>), such that only a single coordinate (say <math>x</math>) is importa
    16 KB (2,453 words) - 18:26, 30 July 2019
  • ArcTetration
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation 78 (2009), 1647-1670. : \( \mathrm{ate}_b(\mathrm{tet}_b(z))=z \)
    7 KB (1,091 words) - 23:03, 30 November 2019
  • Fixed point
    ...cally analytic function with hyperbolic fixpoint at \(0\), i.e. \(f(z)=c_1 z + c_2z^2 + \dots\), \(|c_1|\neq 0,1\), there is always a locally analytic a <math>\sigma(f(z))=c_1 \sigma(z))\</math>
    4 KB (574 words) - 18:26, 30 July 2019
  • B271az.cc
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y);
    3 KB (529 words) - 14:32, 20 June 2013
  • Fslog.cin
    // To call this function at complex argument z, type '''FSLOG(z)''' z_type z=z1-1.; z/=2.;
    5 KB (275 words) - 07:00, 1 December 2018
  • Class of equivalence
    ...(\mathbb Z\) is used to denote the set of integer numbers; \(m \in \mathbb Z\). \( \mathbb N \subset \mathbb Z\)
    7 KB (1,216 words) - 18:25, 30 July 2019
  • Holomorphic function
    ...C\), there is defined function \(f(z) \in \mathbb C\) such that for any \(z \in C\) there exist the derivative ...ystyle f'(z)= \lim_{t \rightarrow 0,~ t\in \mathbb C}~ \frac{f(z\!+\!t)-f(z)}{t}
    1 KB (151 words) - 21:08, 25 January 2021
  • Tania function
    f'(z)= \frac{f(z)}{1+f(z)} ...nd then along the straight line (parallel to the real axis) to the point \(z\).
    27 KB (4,071 words) - 18:29, 16 July 2020
  • LambertW function
    ...nction." From MathWorld--A Wolfram Web Resource. </ref>, is solution \(W=W(z)\) of equations ...tyle \!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (0\mathrm{a}) ~ ~ ~ W'= \frac{W}{(1+W)~z}\)
    8 KB (1,107 words) - 18:26, 30 July 2019
  • Doya function
    In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be expressed through the \mathrm{Doya}(z)=\mathrm{LambertW}\Big( z~ \mathrm{e}^{z+1} \Big)\)
    19 KB (2,778 words) - 10:05, 1 May 2021
  • Doya.cin
    z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
    3 KB (480 words) - 14:33, 20 June 2013
  • Table of superfunctions
    : \( \!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z+1)=T(F(z)) \) : \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \)
    11 KB (1,565 words) - 18:26, 30 July 2019
  • Square root of exponential
    : \(\!\!\!\!\!\!\!\!\!\!\!\!\!(1) ~ ~ ~ \varphi(\varphi(z))=z\) ...) is assumed to be [[holomorphic function]] for some domain of values of \(z\).
    5 KB (750 words) - 18:25, 30 July 2019
  • Quantum Mechanics
    ...ot \</math>1/\sin(z)<math>); and \</math>\exp^2(z)\\]means <math>\exp(\exp(z))\</math>, but not \\[\exp(z)^2\\]and not <math>\exp(z^2)\</math>.</ref>.
    7 KB (1,006 words) - 18:26, 30 July 2019
  • Iteration
    [[File:PowIteT.jpg|400px|thumb|Fig.1. Iterates of \(T(z)=z^2~\): \(~y\!=\!T^n(x)\!=\!x^{2^n}~\) for various \(n\)]] [[File:ExpIte4T.jpg|360px|thumb|Fig.3. Iterates of \(T(z)=\exp(z)~\): \(~y\!=\!T^n(x)\!=\!\exp^n(x)~\) ]]
    14 KB (2,203 words) - 06:36, 20 July 2020
  • Theorem
    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 (248 words) - 14:33, 20 June 2013
  • Natural tetration
    : \(\exp(\mathrm{tet}(z))= \mathrm{tet}(z\!+\!1)\) ...on of the [[Transfer equation]] \( \mathrm{tet}(z\!+\!1)=\exp(\mathrm{tet}(z)) \).
    14 KB (1,972 words) - 02:22, 27 June 2020
  • Квадратный корень из факториала
    : \(f(f(z))=z!\) ...7/home.html D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    6 KB (312 words) - 18:33, 30 July 2019
  • Iterated integral
    D^{-1} \mathrm {e}^{px}=\int_0^x \mathrm{e}^{pz} \mathrm d z ...\(u\) an \(v\) representable in form (6), and \(g(z)=\alpha u(z) + \beta v(z)\)
    9 KB (1,321 words) - 18:26, 30 July 2019
  • Корень из факториала
    : \(h(h(z))=z\) для некоторого домена значений \(z\).
    7 KB (381 words) - 18:38, 30 July 2019
  • Уравнение Шредера
    : \( \!\!\!(1) ~ ~ ~ T(f(z))=f(kz)\) : \(\!\!\!(2) ~ ~ ~ T(F(z))=F(z+1)\)
    5 KB (116 words) - 18:37, 30 July 2019
  • Коррупция
    Евгения Альбац. Кто вы, доктор Z? № 5 (274) от 18 февраля 2013 года.</ref>. Он состои ...ч активистов за компьютерами». Блогер doct-z — о создании глобального проекта по поис
    219 KB (3,034 words) - 19:23, 7 November 2021
  • Filog.cin
    ...\(\exp(z)\) is evaluated with routine complex double Filog(complex double z) below z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
    2 KB (258 words) - 10:19, 20 July 2020
  • Filog
    \(f=\mathrm{Filog}(z)\) is solution of the equation for base \(b\!=\!\exp(z)\).
    4 KB (572 words) - 20:10, 11 August 2020
  • Tetration to Sheldon base
    ...\!\!\! (1) \displaystyle ~ ~ ~ \exp(a~ \mathrm{tet_s}(z)) = \mathrm{tet}_s(z\!+\!1)\) ...ex half-line, except some facility of the negative part of the real axis \(z<-2\); the tetration should have the cutline there.
    5 KB (707 words) - 21:33, 13 July 2020
  • GLxw2048.inc
    ...-5718-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670.</ref>. { int m,j,i; long double z1,z,xm,xl,pp,p3,p2,p1;
    108 KB (1,626 words) - 18:46, 30 July 2019
  • Iterated Cauchi
    T(F(z))=F(z+1) It is assumed that \(F(z)\) is holomorphic at least in the strip \(\Re(z)\le 1\), and
    6 KB (987 words) - 10:20, 20 July 2020
  • Institute for Laser Science
    | doi=10.1007/s00340-005-2083-z http://maps.google.com/maps?q=34.85,138.55&ie=UTF8&om=1&z=19&ll=35.657952,139.54128&spn=0.001077,0.002942&t=h
    12 KB (1,757 words) - 07:01, 1 December 2018
  • Fsexp.cin
    // complex<double>FSEXP( complex <double> z) z_type fima(z_type z){ z_type c,e;
    9 KB (654 words) - 07:00, 1 December 2018
  • Факториал
    : \( F(z)=z\cdot F(z\!-\!1)\) : \(\mathrm{Factorial}(z)=z!\)
    2 KB (59 words) - 18:33, 30 July 2019
  • ArcCos
    : \( \cos(\arccos(z))=z\) ...phic in the whole complex plane except the halflines \(z\!\le\! -1\) and \(z\!\ge\! 1\).
    5 KB (754 words) - 18:47, 30 July 2019
  • ArcCip
    : \(\displaystyle \mathrm {Cip}(z)=\frac{\cos(z)}{z}\) <!-- Complex map of function Cip is shown at right.!--> : \(\displaystyle \mathrm{Cip}(\mathrm{ArcCip}(z))=z\).
    8 KB (1,211 words) - 18:25, 30 July 2019
  • SuperFactorial.cin
    z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    1 KB (88 words) - 14:55, 20 June 2013
  • Fac.cin
    z_type fracti(z_type z){ z_type s; int n; DB a[17]= s=a[16]/(z+19./(z+25./(z))); for(n=15;n>=0;n--) s=a[n]/(z+s);
    4 KB (487 words) - 07:00, 1 December 2018
  • ArcSin
    : \(\displaystyle \sin(z) = \frac{\exp(\mathrm i z)- \exp(-\mathrm i z)}{2~ \mathrm i}\) \(f=\arcsin(z)\) is holomorphic solution \(f\) of equation
    9 KB (982 words) - 18:48, 30 July 2019
  • Coshc
    : \(\displaystyle \mathrm{coshc}(z)=\frac{\cosh(z)}{z}\) : \(\displaystyle \cosh(z)=\cos(\mathrm i z) = \frac{\mathrm e^z+\mathrm e^{-z} }{2}\)
    4 KB (509 words) - 18:26, 30 July 2019
  • ArcCosc
    : \( \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z}\) : \(\displaystyle \mathrm{sinc}(z)=\frac{\sin(z)}{z}\)
    8 KB (1,137 words) - 18:27, 30 July 2019
  • Cosc
    : \( \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z}\) : \( \displaystyle \mathrm{sinc}(z) = \frac{ \sin(z)}{z}\)
    4 KB (649 words) - 18:26, 30 July 2019
  • Wakame
    : \(\!\!\!\!\!\!\!\!\! (4) ~ ~ ~ ~ \mathrm{cohc}(z)=\frac{\cosh(z)}{z}\); ...\!\!\!\! (5) ~ ~ ~ ~ \mathrm{cohc}'(z)=\frac{\sinh(z)}{z}-\frac{\cosh(z)}{z^2}\)
    4 KB (581 words) - 18:25, 30 July 2019

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