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  • :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z\!+\!1)=T(F(z))$ :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \displaystyle F(z) = L+\sum_{n=1}^{N} a_n \varepsilon^n + o(\varepsilon^N)$ , where $\varepsi
    20 KB (3,010 words) - 18:11, 11 June 2022
  • : \(\mathrm{SuperFactorial}(z)=\mathrm{Factorial}^z(3)\) : \(\mathrm{Factorial}(\mathrm{SuperFactorial}(z))=\mathrm{SuperFactorial}(z\!+\!1)\)
    18 KB (2,278 words) - 00:03, 29 February 2024
  • : \(F(z\!+\!1)=h(F(z))\) for all \(z\in C \subseteq \mathbb C\).
    3 KB (519 words) - 18:27, 30 July 2019
  • : \(G(T(z))=G(z)+1\) In certain range of values of \(z\), this equation is equivalent of the [[Transfer equation]]
    4 KB (547 words) - 23:16, 24 August 2020
  • 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
  • : \((1)~ ~ ~ ~ ~ G(T(z))=G(z)+1\) at least for \(z\) from some domain in the complex plane.
    4 KB (598 words) - 18:26, 30 July 2019
  • ...}{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
  • :\( \exp(\ln(z))=z ~ ~\) for all from the range of definition; : \(\exp_b(z)=b^z\)
    4 KB (661 words) - 10:12, 20 July 2020
  • :\(\mathrm{Nest}[f,z,c]\) 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
  • | doi= 10.1007/s00340-005-2083-z | doi= 10.1007/s00340-005-2083-z
    15 KB (2,106 words) - 13:37, 5 December 2020
  • ...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
  • ...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
  • 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
  • ...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
  • 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
  • // 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
  • ...(\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
  • ...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
  • 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
  • ...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
  • 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
  • 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
  • : \( \!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z+1)=T(F(z)) \) : \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \)
    11 KB (1,565 words) - 18:26, 30 July 2019
  • : \(\!\!\!\!\!\!\!\!\!\!\!\!\!(1) ~ ~ ~ \varphi(\varphi(z))=z\) ...) is assumed to be [[holomorphic function]] for some domain of values of \(z\).
    5 KB (750 words) - 18:25, 30 July 2019
  • ...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
  • [[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
  • 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
  • : \(\exp(\mathrm{tet}(z))= \mathrm{tet}(z\!+\!1)\) ...on of the [[Transfer equation]] \( \mathrm{tet}(z\!+\!1)=\exp(\mathrm{tet}(z)) \).
    14 KB (1,972 words) - 02:22, 27 June 2020
  • : \(f(f(z))=z!\) ...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
  • 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
  • : \(h(h(z))=z\) для некоторого домена значений \(z\).
    7 KB (381 words) - 18:38, 30 July 2019
  • : \( \!\!\!(1) ~ ~ ~ T(f(z))=f(kz)\) : \(\!\!\!(2) ~ ~ ~ T(F(z))=F(z+1)\)
    5 KB (116 words) - 18:37, 30 July 2019
  • 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
  • ...\(\exp(z)\) 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
  • \(f=\mathrm{Filog}(z)\) is solution of the equation for base \(b\!=\!\exp(z)\).
    4 KB (572 words) - 20:10, 11 August 2020
  • ...\!\!\! (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
  • ...-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
  • 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
  • | 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
  • // 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
  • : \( F(z)=z\cdot F(z\!-\!1)\) : \(\mathrm{Factorial}(z)=z!\)
    2 KB (59 words) - 18:33, 30 July 2019
  • : \( \cos(\arccos(z))=z\) ...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
  • : \(\displaystyle \mathrm {Cip}(z)=\frac{\cos(z)}{z}\) <!-- 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
  • 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
  • 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
  • : \(\displaystyle \sin(z) = \frac{\exp(\mathrm i z)- \exp(-\mathrm i z)}{2~ \mathrm i}\) \(f=\arcsin(z)\) is holomorphic solution \(f\) of equation
    9 KB (982 words) - 18:48, 30 July 2019
  • : \(\displaystyle \mathrm{coshc}(z)=\frac{\cosh(z)}{z}\) : \(\displaystyle \cosh(z)=\cos(\mathrm i z) = \frac{\mathrm e^z+\mathrm e^{-z} }{2}\)
    4 KB (509 words) - 18:26, 30 July 2019
  • : \( \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z}\) : \(\displaystyle \mathrm{sinc}(z)=\frac{\sin(z)}{z}\)
    8 KB (1,137 words) - 18:27, 30 July 2019
  • : \( \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z}\) : \( \displaystyle \mathrm{sinc}(z) = \frac{ \sin(z)}{z}\)
    4 KB (649 words) - 18:26, 30 July 2019
  • : \(\!\!\!\!\!\!\!\!\! (4) ~ ~ ~ ~ \mathrm{cohc}(z)=\frac{\cosh(z)}{z}\); ...\!\!\!\! (5) ~ ~ ~ ~ \mathrm{cohc}'(z)=\frac{\sinh(z)}{z}-\frac{\cosh(z)}{z^2}\)
    4 KB (581 words) - 18:25, 30 July 2019
  • ...{\cosh(z)}{z} ~,~\) \(~ ~ \displaystyle \mathrm{cosc}(z) = \frac{\cos(z)}{z}\) ...{\sinh(z)}{z} ~,~ \) \(~ ~ \displaystyle \mathrm{sinc}(z) = \frac{\sin(z)}{z} \)
    4 KB (495 words) - 18:47, 30 July 2019
  • : \(\mathrm{acosq}(z)=\mathrm{acosc}\left( \mathrm e ^{\mathrm i \pi/4} \,z \right)\) main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    4 KB (656 words) - 18:25, 30 July 2019
  • // ArcCosc is [[inverse function]] of [[Cosc]]; \(\text{cosc}(z) = \cos(z)/z\). z_type cosc(z_type z) {return cos(z)/z;}
    1 KB (219 words) - 18:46, 30 July 2019
  • : \(\text{acosqq}(z)=\text{acosq}(z)\, \tan\!\!\big( \text{acosq}(z) \big)\) : \(\text{acosq}(z)=\text{acosq}\big( \mathrm e ^{\mathrm i \pi /4}\, z \big)\)
    2 KB (216 words) - 18:26, 30 July 2019
  • z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    3 KB (436 words) - 18:47, 30 July 2019
  • \(f=\mathrm{Acosc1}(z)\) is solution of equation : \( \displaystyle \mathrm{cosc}(f)=z\)
    6 KB (896 words) - 18:26, 30 July 2019
  • : \( \mathrm{Factorial}(\mathrm{ArcFactorial}(z))=z\) However, \(\mathrm{Factorial}^{-1}(z)\) should not be confused with
    3 KB (376 words) - 18:26, 30 July 2019
  • ...\!\!\!\!\!\ (2) ~ ~ ~ \Psi=\Psi( \vec x, z)=\exp(\mathrm i k z)\psi(\vec x,z)\) ...(2) into (1) and neglecting term with second derivative with respect to \(z\) gives
    3 KB (496 words) - 18:25, 30 July 2019
  • ...al case, the particle propagates mainly along some coordinate, let it be \(z\), and the potential depends only on the transversal coordinates. ...\!\!\!\!\!\!\!\!\!\! (6) ~ ~ ~ \psi=\mathrm e ^{\mathrm i (c+\mathrm i s) z }\)
    15 KB (2,070 words) - 18:47, 30 July 2019
  • J_0''(z)+ J_0'(z)/z+
    6 KB (913 words) - 18:25, 30 July 2019
  • ...nc}(z)= \frac{\sin(z)}{z}~\), \(~~\mathrm{sinc}\big(\mathrm{asinc}(z)\big)=z\) : \( \displaystyle \mathrm{acosc}(z^*)= \mathrm{acosc}(z)^*\)
    4 KB (563 words) - 18:27, 30 July 2019
  • ...is assumed, and it is supposed that mainly the particle propagates along \(z\) axis, and \(x\) is called the transversal coordinate.!--> ...psi= \psi(x,z)\) and \(\nabla\) differentiates with respect to \(x\) and \(z\).
    5 KB (743 words) - 18:47, 30 July 2019
  • f''(z)+f(z)/z=f(z) K_0(z) = \exp(-z)\sqrt{\frac{\pi}{2z}} ~ \Big( 1+ O(1/z)\Big)
    3 KB (394 words) - 18:26, 30 July 2019
  • solution \(f=f(z)\) of the Bessel equation f''+f'/z+f=0\)
    3 KB (445 words) - 18:26, 30 July 2019
  • : \(\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ z^2 f''(z) + z f'(z) + (z^2-\nu^2) f(z)=0\) : \(\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ H_\nu(z)=J_\nu(z)+\mathrm i Y_\nu(z)\)
    3 KB (388 words) - 18:26, 30 July 2019
  • : \(\!\!\!\! \mathrm{BesselJ1}(z)=J_1(z)= \mathrm{BesselJ}[1,z]\) f''(z)+f'(z)/z + (z^2\!-\!1)f(z) = 0\)
    3 KB (439 words) - 18:26, 30 July 2019
  • z_type BesselJ0o(z_type z){ int n; z_type c,s,t; s=1.; c=1.; t=-z*z/4.; for(n=1;n<32;n++) {c/=0.+n*n; c*=t; s+=c;}
    2 KB (190 words) - 18:47, 30 July 2019
  • // BesselJ[1,z] implementation: z_type BesselJ1o(z_type z){ int n; z_type c,s,t;
    2 KB (159 words) - 14:59, 20 June 2013
  • \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) Due to singularity of the equation at \(z=0\), the regular solution should have specific behavior. This solution is c
    13 KB (1,592 words) - 18:25, 30 July 2019
  • ...elj0.cin]] is also required for the evaluation of BesselY0(\(z\)) at \(\Re(z) < 0\). z_type BesselY0o(z_type z){ z_type q=z*z, L=log(z),c;
    4 KB (370 words) - 18:46, 30 July 2019
  • [[BesselH0]]\((z)=H_0(z)\!=\)[[HankelH1]]\([0,z]\) is the [[Cylindric function]] H (called also the [[Hankel function]]) o : \(H_0(z)=J_0(z)+\mathrm i Y_0(z)\)
    4 KB (509 words) - 18:26, 30 July 2019
  • The only two spatial coordinates \(Z\) and \(Y\) are used; and the letter \(Z\) is not necessary for the third spatial coordinate. There fore it is used ...!\!\!\!\!\!\!(2) ~ ~ ~ ~ Z=\mathrm{Serega}(z)=z+\mathrm i ~ \exp(\mathrm i z^*)\)
    12 KB (1,879 words) - 18:26, 30 July 2019
  • z_type Serega(z_type z){ DB x,y, p,q, r,s,c; int n; x=Re(z); y=Im(z); z_type ArcSerega(z_type z){ DB x,y ,X,Y,X0,Y0, r,s,c, rc,rs, dX, dY; int n;
    1 KB (265 words) - 15:00, 20 June 2013
  • ...on''' is nongolomorphic function \(\mathrm{Serega}\) of complex variable \(z\) such that : \(F(z)=x+\mathrm i ~ \exp(\mathrm i ~ z^*)\)
    5 KB (674 words) - 18:25, 30 July 2019
  • ...\!\!\!\!\!\!\!\!(1) ~ ~ ~ ~ \mathrm{LogisticOperator}_s(z) = s\,z \,(1\!-\!z)\) where \(z\) is complex number and \(s\) is real number; usually it is assumed that \(
    7 KB (886 words) - 18:26, 30 July 2019
  • z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); }
    3 KB (364 words) - 07:00, 1 December 2018
  • ...\!\!\!\!\!\! (1) ~ ~ ~ T(z)=\mathrm{LogisticOperator}_s(z)= s\, z\, (1\!-\!z)\) ...~ ~ \mathrm{ArcLogisticSequence}_s(T(z))= \mathrm{ArcLogisticSequence}_s(z)+1\)
    3 KB (380 words) - 18:25, 30 July 2019
  • ...\!\!\!\!\!\!\!\!(1) ~ ~ ~ ~ \mathrm{LogisticOperator}_s(z) = s\,z \,(1\!-\!z)\) : \(\!\!\!\!\!\!\!\!\!\!\!(2) ~ ~ ~ ~ F(z\!+\!1)=T(F(z))\)
    6 KB (817 words) - 19:54, 5 August 2020
  • f'(z)= \frac{f(z)}{1+f(z)} ...nd then along the straight line (parallel to the real axis) to the point \(z\).
    4 KB (610 words) - 10:22, 20 July 2020
  • ...ler Institute of Quantum Electronics HPT E 16.3 Auguste-Piccard-Hof 1 8093 Zürich ...\!\!\!\! (1) ~ ~ ~ \mathrm{Keller}(z)=z+ \ln\!\Big(\mathrm e - \mathrm e^{-z}(\mathrm e-1) \Big)\)
    10 KB (1,479 words) - 05:27, 16 December 2019
  • :\( \!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ \mathrm {Shoko}(z)=\ln\Big(1+\mathrm e^z (\mathrm e -1) \Big)\) ...!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \mathrm {Shoko}(z)= (\mathrm e -1) \mathrm e^z+ O(\mathrm e^{2z})\)
    10 KB (1,507 words) - 18:25, 30 July 2019
  • :\( \mathrm{Shoka}(z)=z+\ln\!\Big( \exp(-z) +\mathrm e -1\Big)\) ...=\mathrm{Shoka}^{-1}\) can be expressed as elementary function; for \(|\Im(z)| < \pi\),
    3 KB (421 words) - 10:23, 20 July 2020
  • : \( \displaystyle \mathrm{ArcShoka}(z)= z + \ln\!\left( \frac{\mathrm e^z-1}{\mathrm e-1} \right)\) :\( T(F(z))=F(z\!+\!1)\)
    3 KB (441 words) - 18:26, 30 July 2019
  • ...\!\!\!\! (1) ~ ~ ~ \mathrm{Keller}(z)=z+ \ln\!\Big(\mathrm e - \mathrm e^{-z}(\mathrm e-1) \Big)\) ...left( \frac{1}{\mathrm e}+\frac{\mathrm e \!-\!1}{\mathrm e}\, \mathrm e^{-z} \right)\)
    4 KB (545 words) - 18:26, 30 July 2019
  • z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    1 KB (88 words) - 15:01, 20 June 2013
  • z_type infp0(z_type z) s=c[29]; for(n=28;n>=0;n--){ s*=z; s+=c[n];} return s;}
    3 KB (353 words) - 15:01, 20 June 2013
  • z_type afacb(z_type z){ z_type t=(log(z)-F0)/c2; z_type v=sqrt(t);
    995 bytes (148 words) - 18:46, 3 September 2023
  • z_type arcsuperfac0(z_type z){ int n; z_type s, c, e; // z-=2.; s=U[15]*z; for(n=14;n>=0;n--){ s+=U[n]; s*=z;}
    1 KB (124 words) - 15:01, 20 June 2013
  • z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));
    1 KB (139 words) - 18:48, 30 July 2019
  • z_type f45L(z_type z){ int n; z_type e,s; z-=4.;
    2 KB (163 words) - 18:47, 30 July 2019
  • (1) \(~ ~ ~ \mathrm{ArcLambertW}(z) = \mathrm{zex}(z) = z \exp(z) \) In wide ranges of values of \(z\), the relations
    3 KB (499 words) - 18:25, 30 July 2019
  • ...on]] of [[ArcLambertW]], denoted also as [[zex]], \(\mathrm{zex}(z)=z \exp(z)\). ...\!\!\!\!(2) ~ ~ ~ \mathrm{SuZex}(z\!+\!1)=\mathrm{zex}\Big(\mathrm{SuZex}(z)\Big)\)
    7 KB (1,076 words) - 18:25, 30 July 2019
  • ..., и тогда, например, выражения \(f(0)\) или \(f(z)\) имеют не больше смысла, чем запись \(\displa
    8 KB (210 words) - 18:33, 30 July 2019
  • z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
    1 KB (209 words) - 15:01, 20 June 2013
  • ...of function [[SuZex]], which is [[superfunction]] of [[zex]]\(\,(z)=z\exp(z)~\). The [[complex map]] of [[SuZex]] is shown in figure at right. Below, i (1) \(~ ~ ~ T(z)=\mathrm{zex}(z) = z\,\exp(z)~\)
    14 KB (2,037 words) - 18:25, 30 July 2019
  • ...x_1)=a[0][0]/z + (a[1][0]+a[1][1]L)/z^2 + (a[2][0]+a[2][1] L + a[2][2]L^2)/z^3 + .. // and L=Log[z] or L=Log[-z]
    6 KB (180 words) - 15:01, 20 June 2013
  • ...is [[superfunction]] for the [[transfer function]] T(z)=[[zex]](z)= z exp(z) <br> z_type zex(z_type z) { return z*exp(z);}
    12 KB (682 words) - 07:06, 1 December 2018
  • z_type LambertWo(z_type z){ int n,m=48; z_type d=-z; return z*(1.+s); }
    5 KB (287 words) - 15:01, 20 June 2013
  • // z_type zex(z_type z) { return z*exp(z) ; } z_type AuZexAsy(z_type z){ int m=15,n; z_type s;
    3 KB (274 words) - 15:01, 20 June 2013
  • ...o [[Abel function]] for the [[transfer function]] \(\mathrm{zex}(z)=z \exp(z)\). ...]] is [[Inverse function]] of [[SuZex]], so, in wide ranges of values of \(z\), the relations
    6 KB (899 words) - 18:44, 30 July 2019
  • (1) \(~ ~ ~ \mathrm{pow}_a(z) = z^a = \exp_z(a) = \exp(a \ln(z))\) ...is assumed that \(a\) is real. The real-real plot of function \(T(z)\!=\!z^a\) is shown in Fig.1 for several values of \(a\).
    15 KB (2,495 words) - 18:43, 30 July 2019
  • \(~\mathrm{Tra}(z)=\mathrm e^z +z~\) ...hrm{ArcTra}(z)=\) \(z-\mathrm{Tania}(z\!-\!1)=\) \( z-\mathrm{WrightOmega}(z)\)
    9 KB (1,320 words) - 11:38, 20 July 2020
  • \( \!\!\!(1) ~ ~ ~ T(f(z))=f(kz)\)<br>
    3 KB (47 words) - 18:36, 30 July 2019
  • (1) \(~ ~ ~ g\Big(T(z)\Big)= s \, g(z)\) ...se \(~s~\) from both sides of equation (1), assuming that \(~s~\) and \(~g(z)~\) are not real negative number nor zero. This gives
    8 KB (1,239 words) - 11:32, 20 July 2020
  • (1) \(~ ~ ~ t_r^m(z)=T^n(z)~\) for all \(~z~\) in some vicinity of \(~L~\).
    2 KB (272 words) - 18:25, 30 July 2019
  • (1) \(~ ~ ~ T\big(f(z)\big)= f( K\, z)~\) (2) \(~ ~ ~ g\big(T(z)\big)= K \, g(z) \)
    10 KB (1,627 words) - 18:26, 30 July 2019
  • ...is supposed to be [[fractional iterate]] of function \(T\), id est, for \(z\) in vicinity of point \(L\), (1) \( ~ ~ ~ f^n(z)=T^m(z)\)
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  • </ref> of the [[Trappmann function]], \(~\mathrm{tra}(z)=z+\exp(z)~\). ...behaves as \(z\rightarrow -\ln(-z)\) at large \(z\) for the most of \(\arg(z)\), id set, in the whole complex plane except the strip along the real axis
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  • z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    2 KB (119 words) - 07:06, 1 December 2018
  • ...values of z, \(\rm AuFac(Sufac(z))\!=\!z~\) and \(~\rm SuFac(Aufac(z))\!=\!z~\). z_type arcsuperfac0(z_type z){ int n; z_type s, c, e;
    2 KB (137 words) - 18:46, 30 July 2019
  • (1)\(~ ~ ~ \mathrm{tra}(z)=z+\exp(z)\) (2) \(~ ~ ~ \mathrm{ArcTra}(z)=z-\mathrm{Tania}(z-1)\)
    10 KB (1,442 words) - 18:47, 30 July 2019
  • ...[[Abel function]] of the [[Trappmann function]], \(\mathrm{tra}(z)=z+\exp(z)\). \( \mathrm{AuTra} \Big( \mathrm{tra}(z) \Big)= \mathrm{AuTra}(z)+1\)
    6 KB (1,009 words) - 18:48, 30 July 2019
  • z_type arctra(z_type z){return z-Tania(z-1.);} z_type tra(z_type z) {return z+exp(z);}
    1 KB (197 words) - 15:03, 20 June 2013
  • z _type f4ten(z_type z){ //NOT SHIFTED FOR x1 !!!! ...){t=Aten*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}
    2 KB (287 words) - 15:03, 20 June 2013
  • ...=\exp(a)\) for \(0.05<a<2\) ; \(\mathrm{tet}_b(z)\) is approximated for \(|z|<1\) using the fruncated Taylor expansion of // \(\mathrm{tet}_b(z) - \ln(z+2)\)
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  • T(z)=q\cdot z \cdot (1-z) <math> F(z\!+\!1)=T(F(z))
    3 KB (411 words) - 18:26, 30 July 2019
  • http://vk.com/club32160205?z=photo-32160205_304217834%2Fwall-32160205_6475 http://vk.com/club32160205?z=photo-32160205_304216982%2Fwall-32160205_6470
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  • Soudek P, Valenová S, Vavríková Z, Vanek T.
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  • ...kolí? No ano, hlavně USA. Jak nejefektivněji dosáhnou USA toho, že se z Ruska stane slabá země? Správně, dosadí na nejvyšší post svého age
    12 KB (1,939 words) - 07:04, 1 December 2018
  • ...kolí? No ano, hlavně USA. Jak nejefektivněji dosáhnou USA toho, že se z Ruska stane slabá země? Správně, dosadí na nejvyšší post svého age
    86 KB (1,212 words) - 05:03, 28 February 2023
  • D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
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  • <br>This function returns the sum of the complex numbers a and b, z=a+b. ...<br> This function returns the difference of the complex numbers a and b, z=a−b.
    6 KB (975 words) - 18:47, 30 July 2019
  • ...unction]] for the [[power function]], id est, transfer function \(T(z)\!=\!z^a\) For the transfer function \(T(z)\!=\!z^a\), the two superfunctions
    3 KB (470 words) - 18:47, 30 July 2019
  • \lim_{z\rightarrow 0}~ \Big( \theta(x\!+\!y\!+\!z)-\theta(x\!-\!y\!-\!z) \Big)
    38 KB (6,232 words) - 18:46, 30 July 2019
  • T[z_] = z + z^3 + q z^4 F[m_, z_] := 1/(-2 z)^(1/2) (1 - q/(-2 z)^(1/2) + Sum[P[n, Log[-z]]/(-2 z)^(n/2), {n, 2, m}])
    16 KB (1,450 words) - 06:58, 1 December 2018
  • ...RI to denote holomorphic function, that in vicinity of the real axis \(\Re(z\ge 0\)) can be expressed through the [[morinaga function]] mori: \(\mathrm{nori}(z)=\mathrm{mori}\big( \sqrt{z} \big) ^2=\,\)
    13 KB (1,759 words) - 18:45, 30 July 2019
  • ...ukrainischen Präsidenten Petro Poroschenko gesagt haben, dass seine Armee zügig osteuropäische Hauptstädte erreichen könnte. Das geht aus einer Ges ...kolí? No ano, hlavně USA. Jak nejefektivněji dosáhnou USA toho, že se z Ruska stane slabá země? Správně, dosadí na nejvyšší post svého age
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  • \(f(z+1)=\ln(f(z))\) \(f(z)=\mathrm{tet}(-z)\)
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  • ...'superpower function''' is [[superfunction]] for [[power function]] \(T(z)=z^a\) where \(a\) is parameter; often it is assumed, that \(a\!>\!1\). \(\mathrm{SuPow}_a(z)=\exp(a^z)\)
    6 KB (903 words) - 18:44, 30 July 2019
  • ...ction]] of function [[sin]], \(\mathrm{SuSin}(z\!+\!1)=\sin(\mathrm{SuSin}(z))\). z_type susin0(z_type z){ z_type d,c,L;
    3 KB (269 words) - 18:48, 30 July 2019
  • ...ch is superfunction of the [[Trappmann function]] \(\mathrm{tra}(z)=z+\exp(z)\). // sutran(z) returns value \(\mathrm{SuTra}(z)\) with at least 14 decimal digits, except vicinity of the positive part of
    3 KB (351 words) - 18:48, 30 July 2019
  • <math> \displaystyle f(z)=\frac{1}{2\pi \mathrm i} \oint \frac{f(t)}{t-z} \mathrm d t</math> D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670.
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  • \(\mathbb J(f) = \{ z \in C : \exists ~ n\in \mathbb N_+ ~:~ f^n(z) \bar \in C\}\) \(\mathbb F(f) = \{ z \in C : \forall ~ n\in \mathbb N_+ ~,~ f^n(z) \in C\}\)
    4 KB (630 words) - 18:44, 30 July 2019
  • z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    2 KB (131 words) - 18:47, 30 July 2019
  • z_type arcsuperfac0(z_type z){ int n; z_type s, c, e; // z-=2.; s=U[15]*z; for(n=14;n>=0;n--){ s+=U[n]; s*=z;}
    2 KB (202 words) - 06:58, 1 December 2018
  • g(z)=P(f(Q(z)))=P\circ f\circ Q (z) ...as the superscript; conjugation of a complex number \(z\) is written as \(z^*\).
    6 KB (921 words) - 18:46, 30 July 2019
  • ...pplied sequentially, one by one, in raw, for example, <math>A\Big(B\big(C(z)\big)\Big)</math>. :<math> \{ z \in \mathbb{C} : \Im(z)\ge 0 \} </math>.
    5 KB (753 words) - 18:47, 30 July 2019
  • \( P_c(z)=z^2+c\) \(\Phi(z)=p(F(z))\)
    2 KB (229 words) - 18:44, 30 July 2019
  • ...of exponential]] (or [[Iteration of exponent]]) is function \(f(z)=\exp^n(z)\), where upper superscript indicates the number of iteration. ...th \(n = \pm 2\); \(\exp^2(z)=\exp(\exp(z))\), and \(\exp^{-2}(z)=\ln(\ln(z))\).
    7 KB (1,161 words) - 18:43, 30 July 2019
  • [[File:Fracit05t150.jpg|300px]]\( t(z)=\frac{z}{0.5+z}~\); \(~y=t^n(x)\) versus \(x\) for various \(n\) [[File:Fracit10t150.jpg|300px]]\( t(z)=\frac{z}{1+z} ~\); \(~y=t^n(x)\) versus \(x\) for various \(n\)
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  • \((1) ~ ~ ~ \displaystyle T(z)=\frac{u+v z}{w+z}\) \((2) ~ ~ ~ \displaystyle A+B z= \lim_{M\rightarrow \infty} \frac{M A+ M B}{M+z}\)
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  • \(T(F(z))=F(z+1)\) \(G(T(z))=G(z)+1\)
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  • [[File:Itelin125T.jpg|440px|thumb|Iterates of \(T(z)=A+Bz~\) at \(~A\!=\!1\), \(B\!=\!2~\); \(~y=T^n(x)~\) versus \(x\) for var \((1) ~ ~ ~ T(z)=A+B z\)
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  • \(\mathrm{mori}(z)=\displaystyle \frac{ J_0 (L_1 z)}{1-z^2}\) For integer \(m>0\) and \(|z|\gg 1\), function [[mori]]\((z)\) can be approximated with
    3 KB (456 words) - 18:44, 30 July 2019
  • ...ven integer number \(n\), called "number of Ackermann", function \(A_{b,n}(z)\) is called [[Ackermann function]], iff it satisfies the following equatio \(A_{b,1}(z)=b+z\)
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  • \(\mathrm{AdPow}_a(z)=\log_a(\ln(1/z))\) \(\mathrm{AdPow}_a(z)=\log_a(\ln(z))\)
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  • \(\mathrm{Amos}(z)=\) \(\displaystyle ...ac{1}{2}\mathrm{Lof}(z)-\mathrm{Lof}\Big(\frac{z}{2}\Big)-\frac{\ln(2)}{2} z \right)\)
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  • where \(\psi_n(z)=\frac{1}{\sqrt{N_n}}\)[[HermiteH]]\(_n(z)\, \exp(-z^2/2)\) is [[oscillator function]], \(\mathrm{lof}(z)= \ln(\mathrm{Factorial}(z)) = \ln(z!)\)
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  • // In order to evaluate the approximation at artument \(z\), type <b> F3(z) </b> z_type F3(z_type z){ DB x=Re(z);
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  • \(\mathrm{ArcTania}(z)=z+\ln(z)−1\) ...style \mathrm{Tania}^{\prime}(z)=\frac{\mathrm{Tania}(z)}{1+\mathrm{Tania}(z)} \)
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  • z_type asin0(z_type z){ int m,M; z_type q,s; DB c[41]={ M=40; q=z*z; s=c[M]*q; for(m=M-1;m>0;m--) {s+=c[m]; s*=q;}
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  • z_type tra(z_type z){ return z+exp(z);} z_type arctra1(z_type z){ static DB c[22]={0.,0.5,-0.0625,.005208333333333333, // 0 - 3
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  • \(\mathrm{Nem}(\mathrm{ArqNem}(z))=z\) \(\mathrm{Nem}(z)=\mathrm{Nem}_{q}(z)=z+z^3+qz^4\)
    7 KB (1,319 words) - 18:46, 30 July 2019
  • // arcnem(z) evaluates \(\mathrm{ArcNem}_Q(z)\), while parameter \(Q\) should be stored as global variable, together wit z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); }
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  • [[File:Aunemplot.jpg|300px|thumb|Fig.1: \(y\!=\!\mathrm{AuNem}_q(z)\) for ...[[Abel function]] of the [[Nemtsov function]], \(\mathrm{Nem}_q(z)=z+z^3+q z^4 ~ ~\), where \(q~\) is positive parameter.
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  • \(\mathrm{AdPow}_a(z)=\log_a(\ln(z))\) \(\mathrm{AdPow}_a(z)=\log_a(\ln(1/z))\)
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  • \(\mathrm{AuSin}(\sin(z))=\mathrm{AuSin}(z)+1\) \(\mathrm{AuSin}(z)=\mathrm{AuSin}(\pi/2-z)\)
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  • z_type ausin0(z_type z){ z_type b,d,L; int n,N; DB c[32]= N=21; L=log(z); b=z*z; //d=b*(c[N]*.5);
    1 KB (156 words) - 06:58, 1 December 2018
  • \tilde F(z)=\mathrm e\cdot\left(1-\frac{2}{z}\left( 1+\sum_{m=1}^{M} \frac{P_{m}\big(-\ln(\pm z) \big)}{(3z)^m}
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  • ...omplex plane except \(z\le 0\), the relation \(\exp_b\big( \log_b(z) \big)=z\) takes place. \(\log_b\big( \exp_b(z)\big) =z \)
    3 KB (557 words) - 18:46, 30 July 2019
  • ...in(z))=z holds. Iteration of sin is expressed with sinˆn(z)=SuSin(n+AuSin(z)), where the number n of iteration has no need to be integer. .. D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
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  • z_type e1egf(z_type z){ int n,N; z_type c,f; // z+= 2.798248154231454;
    2 KB (219 words) - 18:48, 30 July 2019
  • z_type E1EGI(z_type z){ z_type p; int n; DO(n,18){ p=z-M_E; if(abs(p)<.3) break; z=log(z)*M_E; }
    2 KB (148 words) - 18:47, 30 July 2019
  • z_type e1etf(z_type z){ int n,N; z_type c,f; z+=2.798248154231454;
    2 KB (203 words) - 18:48, 30 July 2019
  • z_type E1ETI(z_type z){ z_type p,q,r,u,v; DB a,b,c; int n; ...DO(n,16){ p=M_E-z; if(abs(p)<.6) break; if(Re(z)>1.e8) break; z=exp(z/M_E); }
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  • \(A_{b,n}(z\!+\!1)=A_{b,n-1}\!\big( A_{b,n}(z)\big)\) ..., the real–holomorphism of ackermanns is assumed, \(A_{b,n}(z^*)=A_{b,n}(z)^*\).
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  • F(z\!+\!1)=T(F(z)) \( \displaystyle \lim_{z\rightarrow \infty} F(z)=L\)
    11 KB (1,715 words) - 18:44, 30 July 2019
  • \(\exp'(z)=z\)
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  • z_type f15(z_type z){ //NOT SHIFTED FOR x1 !!!! ...K){t=A15*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}
    2 KB (272 words) - 07:00, 1 December 2018
  • ...in [[Mathematica]] that evaluates the natural [[tetration]] tet; call SEXP[z] <poem> *) (* c[x_, y_, z_] = RGBColor[x, y, z]; *)
    7 KB (306 words) - 07:00, 1 December 2018
  • ...tine in Mathematica that evaluates the natural arctetration tet; call SLOG[z] <poem> *) slo[z_] := Sum[Extract[DE, n+1] ((z-1)/2)^n, {n,1,90}] + Log[z-Zo]/Zo + Log[z-Zc]/Zc + Extract[DE,1]
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  • { int m,j,i; long double z1,z,xm,xl,pp,p3,p2,p1; { z=cos(M_PI*(i-0.25)/(n+0.5));
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  • void imtqlx ( int n, double d[], double e[], double z[] ); void imtqlx ( int n, double d[], double e[], double z[] )
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  • [[Hermite Gauss mode]] refers to the specific solution \(F=F(x,z)\) of equation then, assuming some large positive \(M\), expression \(M^2 z/k\) has sense of the coordinate along the propagation of wave, and \(M x/k\
    8 KB (1,216 words) - 18:43, 30 July 2019
  • \(\displaystyle h_n(z)= \frac{1}{\sqrt{N_n}} \mathrm{HermiteH}[n,x]=\frac{H_n(x)}{\sqrt{N_n}}\)
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  • ...\(f\) is sigh function \(g\!=\!f^{-1}\), that in wide range of argument \(z\), \(f(g(z))\!=\!z\)
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  • Gazeta Polska, Nr 34 z 20 sierpnia 2014.
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  • F(z+1)=\exp(F(z)) F(z)=L+\exp(L z)+\sum_{n=2}^{M_0} a_{0,n} \exp(L n z) + O(\exp(L (M_0\!+
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  • For \(z\ne 1~\), \(~ ~\mathrm{kori}(z)=\displaystyle \frac{J_0\big(L\, \sqrt{x}\big)}{1-z}\)
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  • For \(z\ne1\), function [[kori]] appears as \(\mathrm{kori}(z)=\displaystyle \frac{J_0\big( L_1 \sqrt{z} \big)}{1-z}\)
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  • \mathrm{nori}(z) \approx \mathrm{korifit76}(z)^2\)
    4 KB (644 words) - 18:47, 30 July 2019
  • ...function [[korifit76]], that approximates function [[kori]]\((z)\) for \(|z|<40\).
    914 bytes (87 words) - 18:48, 30 July 2019
  • TeXForm[TableForm[Table[Table[LaguerreL[n, m, z], {n, 0, 5}], {m, 0, 8}]]] 1 & 1-z & \frac{1}{2} \left(z^2-4 z+2\right) &
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  • ...s with respect to \(n\)th coordinate, where \(n\) = "\(x\)", "\(y\)" or "\(z\)", and the Schroediner equation for the hydrogen atom. \(z= r \sin(\theta)\)
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  • \mathrm{LegendreP}_\ell(z) = \frac{1}{2^\ell \ell !} \frac{\mathrm d\, (z^2\!-\!1)^\ell }
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  • \mathrm{LegendreP}_n(z) = \frac{1}{2^n n!} \frac{\mathrm d\, (z^2\!-\!1)^n }
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  • http://wiadomosci.onet.pl/tylko-w-onecie/prezes-ipn-sowieckie-pomniki-znikna-z-polskich-miast/p5j7g7 [[Katarzyna Szewczuk]]. Prezes IPN: sowieckie pomniki znikną z polskich miast. //
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  • http://www.tvn24.pl/niepublikowane-nagranie-z-kokpitu-tu-154m,636030,s.html ...Tu-154M do Smoleńska. Jest połączeniem trzech ścieżek dźwiękowych: z mikrofonu i radia dowódcy, drugiego pilota i mikrofonów w kabinie. (http:
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  • \ln'(z)=\frac{1}{z}\) \(\ln(z)=\exp^{-1}(z)\)
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  • ...~\) , that is holomorphic in the most of the complex \(z\) plane (except \(z\!\le\!-1\)). While the real part of the argument \(z\) dominates,
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  • \(\mathrm {maga}(z)=1-\mathrm{nagc}(z)^2-\mathrm{nags}(z)^2\) ...ation should be chosen in the integrals for [[nagc]]\((z)\) and [[nags]]\((z)\) in order to provide the convergence.
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  • D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
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  • (M2): ∀x,y,z∈A: d(x,y)+d(y,z)≥d(x,z) such that for any <math>x, y, z \in M</math>, the following holds:
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  • z_type morias(z_type z){ int k,m,n; z_type s,c,t,x; x=1./(z*z); t=-sqrt(2./M_PI/L1/z)/z/z;
    2 KB (188 words) - 07:03, 1 December 2018
  • where \(J_0\) is the zeroth [[Bessel function]], id est, [[BesselJ0]]; \(J_0(z)\!=\,\)[[BesselJ]]\([0,x]\) \mathrm{morias}_m(z) = - \sqrt{\frac{2}{\pi L_1}} z^{-5/2} \, G_m(z^2)\,
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  • [[mori]]\((z)\approx\,\)[[morias]]\(_m(z)~\), \(~z\rightarrow \infty\), with integer \(m\) and \mathrm{morias}_m(z) = - \sqrt{\frac{2}{\pi L_1}} z^{-5/2} \, G_m(z^2)\,
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  • \(\mathrm{Nem}_q(z)=z+z^3+qz^4\) \(\mathrm{Nem}_q'(z)=1+3z^2+4qz^3\)
    4 KB (618 words) - 18:46, 30 July 2019
  • ...m}_q\) is real–holomorphic, id est, \(\mathrm{Nem}_q(z^*)=\mathrm{Nem}_q(z)^*\); this simplifies the consideration. \(\mathrm{Nem}_q(z)=z+z^3+q z^4\)
    3 KB (400 words) - 18:48, 30 July 2019
  • ...Then, Nemtsov Function \(\mathrm{Nem}\) is defined for complex argument \(z\) as follows: (1)\(~ ~ ~ ~ ~ ~ \mathrm{Nem}_q(z)= z+z^3+q z^4\)
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  • \mathrm{sinc}(z)=\frac{\sin(z)}{z} \(\displaystyle \mathrm{sink}(z)=\mathrm{sink}(\pi z)=\frac{\sin(\pi z)}{\pi z}\)
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  • [[qua]]\)(x)=\int_0^x \sqrt{1-z^2}\,\mathrm d z= \( \)
    6 KB (846 words) - 18:47, 30 July 2019
  • ...lation of parabolic coordinates \(u,v\) with Cartesian coordinates \(\rho, z\) can be expressed with the following relation: \(\displaystyle z=\frac{u\!-\!v}{2}\)
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  • \(\mathrm{pen}_b(z)=A_{b, 5}(z)\) \(\mathrm{pen}(z)=\mathrm{pen}_\mathrm e(z)\).
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  • D.Kouznetsov. Solutions of F(z+1)=exp(F(z)) in the complex z plane. Mathematics of Computation, 78 (2009) 1647-1670 William Paulsen and Samuel Cowgill. Solving \(F(z+1)=b^{F(z)}\) in the complex plane. Advances in Computational Mathematics, 2017 March
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  • (1)\(~ ~ ~ F(z+1)=T(F(z))= c~ F(z)~ \Big(1-F(z)\Big)\)
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  • \(z=\sin(\phi)\) \(~\displaystyle \lambda = \frac{Z e^2}{\hbar} \sqrt{\frac{-\mu}{2 E}\,}\)
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  • \(\exp(\mathrm{tet}(z))=\mathrm{tet}(z\!+\!1)\), satisfying certain additional conditions (see [[Superfunctions]] ...-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.
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  • ...e [[superfunction]] of the [[power function]] \(~z\mapsto z^a\!=\!\exp(\ln(z) \,a)~\) \(\mathrm{SdPow}_a(z)=\exp(a^z)\)
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  • Kori[z_]=BesselJ[0,BesselJZero[0,1] Sqrt[z]]/(1-z) naga[p_] = Assuming[{Im[p] == 0}, Integrate[Kori[z]^2 Exp[I p z], {z, 0, Infinity}]]
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  • \(f''(z)+f(z)=0\) \sin(z)= \frac{\exp(\mathrm i z)-\exp(-\mathrm i z)}{2 ~ \mathrm i }\)
    4 KB (680 words) - 18:43, 30 July 2019
  • ...uate \(\mathrm{tet}_{\sqrt{2}}(z)\), the routine should be called as F21E(z) z_type f21E(z_type z){int n; z_type e,s;
    1 KB (109 words) - 18:48, 30 July 2019
  • //z_type tq2L(z_type z){ int n; z_type e,s,k; z_type f21L(z_type z){ int n; z_type e,s,k;
    1 KB (145 words) - 18:47, 30 July 2019
  • ...uate \(\mathrm{tet}_{\sqrt{2}}(z)\), the routine should be called as F23E(z) z_type f23E(z_type z){int n; z_type e,s; DB coefd[24];
    2 KB (146 words) - 18:47, 30 July 2019
  • ...uate \(\mathrm{tet}_{\sqrt{2}}(z)\), the routine should be called as F23L(z) z_type f23L(z_type z){ int n; z_type e,s,k;
    2 KB (168 words) - 18:47, 30 July 2019
  • z_type f43E(z_type z){int n; z_type e,s; DB coeud[23]; e=exp(.32663425997828098238*(z+1.90057764535874));
    1 KB (131 words) - 10:44, 24 June 2020
  • z_type f43L(z_type z){ int n; z_type e,s; z-=4.;
    1 KB (124 words) - 18:46, 30 July 2019
  • z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));
    1 KB (108 words) - 18:47, 30 July 2019
  • z_type f45L(z_type z){ int n; z_type e,s; z-=4.;
    1 KB (131 words) - 18:47, 30 July 2019
  • \(\mathrm{StraR}_q(z)=\sqrt{27 (q\! -\! z)^2 + 4 (1\!+\! 4 q z)^3} \) <!-- = \sqrt{4 + 27 q^2 - 6 q z + 27 z^2 + 192 q^2 z^2 + 256 q^3 z^3} !-->
    4 KB (646 words) - 18:47, 30 July 2019
  • \(\mathrm{Nem}_{q}(z)=z+z^3+qz^4\) \(\mathrm{Nem}_{q}\big( \mathrm{SuNem}_{q}(z)\big)=\mathrm{SuNem}_{q}(z\!+\!1)\).
    6 KB (967 words) - 18:44, 30 July 2019
  • ...e [[superfunction]] of the [[power function]] \(~z\mapsto z^a\!=\!\exp(\ln(z) \,a)~\) \(\mathrm{SuPow}_a(z)=\exp(a^z)\)
    3 KB (405 words) - 18:43, 30 July 2019
  • \((1)~ ~ ~ \mathrm{SuSin}(z\!+\!1)= \sin(\mathrm{SuSin}(z))\) with specific behaviour at infinity, namely, at large \(|z|\),
    15 KB (2,314 words) - 18:48, 30 July 2019
  • // z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } // z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); } // WARNING: Q is global!
    1 KB (228 words) - 07:06, 1 December 2018
  • z_type nem(z_type z){ return z + z*z*z*(NEMTSOVp+z*NEMTSOVq); } //new ...{ int m,n,k; z_type c[22],s; z_type L=log(-z); z_type x=sqrt(-.5/(NEMTSOVp*z));
    2 KB (347 words) - 07:06, 1 December 2018
  • z_type f4(z_type z){ //NOT SHIFTED FOR x1 !!!! ...k,K){t=A*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}
    2 KB (262 words) - 07:06, 1 December 2018
  • z_type f4(z_type z){ //NOT SHIFTED FOR x1 !!!! ...k,K){t=A*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}
    3 KB (439 words) - 07:06, 1 December 2018
  • z_type naiv49(z_type z) // polynonial approximation of tetration z_type s=1.,t=z;
    2 KB (101 words) - 14:55, 12 July 2020
  • ...билей наклейки с фашистской символикой ("Z") и бегут в соседние страны (где им совсем
    21 KB (344 words) - 22:15, 1 October 2022
  • [[File:BubnovFront-z-400.jpg|200px|thumb|[[Бубнов Олег Юрьевич]] <ref name="mev
    28 KB (194 words) - 07:09, 1 December 2018
  • 88 KB (1,587 words) - 11:26, 13 August 2023
  • https://vk.com/publicya_geroy?z=photo-78250853_341031081%2Falbum-78250853_00%2Frev
    46 KB (475 words) - 07:14, 1 December 2018
  • D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    10 KB (139 words) - 07:15, 1 December 2018
  • ...się sankcji. Oligarchowie wycofują pieniądze z Londynu, zwykli Rosjanie z banków) Радзивинович пишет:
    6 KB (101 words) - 18:38, 30 July 2019
  • http://www.tvn24.pl/niepublikowane-nagranie-z-kokpitu-tu-154m,636030,s.html ...Tu-154M do Smoleńska. Jest połączeniem trzech ścieżek dźwiękowych: z mikrofonu i radia dowódcy, drugiego pilota i mikrofonów w kabinie. (http:
    22 KB (754 words) - 00:21, 26 November 2023
  • \(T(F(z))=F(z+1)\) ...(желательно обширной) области значений \(z\).
    19 KB (1,132 words) - 20:36, 16 July 2023
  • \((1) ~ ~ ~ F(z\!+\!1)=T(F(z))\) \((2) ~ ~ ~ G(T(z))=G(z)+1\)
    8 KB (260 words) - 18:36, 30 July 2019
  • ...-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.
    12 KB (240 words) - 18:36, 30 July 2019
  • \(\mathrm{Nem}_q(z)=z+z^3+qz^4\) Solve[ f+f^3+q f^4=z, f]
    6 KB (1,099 words) - 18:46, 30 July 2019
  • \(\mathrm{Nem}_q(z)=z+z^3+qz^4\) Solve[ f+f^3+q f^4=z, f]
    3 KB (524 words) - 18:47, 30 July 2019
  • 30. http://thomas.loc.gov/cgi-bin/query/z?c111%3AH.RES.1489%3A Mr.KING. Bill Text 111th Congress (2009-2010) H.RES.14 http://budclub.ru/z/zhmurikow_e_i/gosperevorot.shtml Е.И.Жмуриков. Можно ли в
    61 KB (1,258 words) - 16:05, 1 December 2018
  • \(~\mathrm{Nem}_q(z)=z+z^3+qz^4 \,\); \(~\) \(\varphi(\varphi(z))\!=\!\exp(z)\). The problem of iteration
    15 KB (2,392 words) - 11:05, 20 July 2020
  • https://vk.com/z.sverdlova ...ажение [[колорад]]ской ленты в виде буквы Z. Использование буквы V вместо русских бук
    64 KB (695 words) - 14:05, 5 May 2022
  • 30. http://thomas.loc.gov/cgi-bin/query/z?c111%3AH.RES.1489%3A Mr.KING. Bill Text 111th Congress (2009-2010) H.RES.14 http://budclub.ru/z/zhmurikow_e_i/gosperevorot.shtml Е.И.Жмуриков. Можно ли в
    62 KB (1,315 words) - 16:08, 1 December 2018
  • 2060. Стена! Z - поколение. Что дальше?
    73 KB (1,064 words) - 07:55, 30 September 2021
  • [[File:BubnovFront-z-400.jpg|180px|thumb|[[Бубнов Олег Юрьевич]] <ref name="mev
    20 KB (119 words) - 10:51, 11 December 2018
  • ...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>.
    6 KB (913 words) - 16:02, 26 July 2019
  • \(\exp_b(z)=b^z=\exp\big(\ln(b) z\big)\) In wide range of values of \(z\), the identity holds,
    887 bytes (130 words) - 18:45, 30 July 2019
  • 49 KB (576 words) - 18:47, 30 July 2019
  • ...и против Украины.// "Список не закончен", - Z-пропагандист Мардан признал, что Украино
    31 KB (818 words) - 02:02, 16 October 2023
  • \( p\!+\!\mathrm{i} q=\varphi(z) \) by Abstract — The holomorphic function h is constructed such that h(h(z))=z! ; this function is interpreted as square root of Factorial.
    12 KB (1,732 words) - 14:01, 12 August 2020
  • \( I(z)= I(0) \exp(-\mu z) \)
    2 KB (301 words) - 23:50, 18 August 2019
  • 934 KB (1,144 words) - 21:14, 11 October 2019
  • \( \varphi(\varphi(z)) = \exp(z) \) \( \varphi(z)= \mathrm{tet}\left( \frac{1}{2} + \mathrm{ate}(z) \right) \)
    3 KB (356 words) - 16:33, 7 January 2020
  • ...per we will consider the tetration, defined by the equation \( F(z+1)= b^F(z)\) in the complex plane with \( F(0)=1\), for the case where \(b\) is compl ...lso develop iteration methods for numerically approximating the function F(z), both for bases inside and outside the Shell-Thron region. ..
    7 KB (1,082 words) - 07:03, 13 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.
    101 KB (14,271 words) - 20:58, 25 September 2020
  • z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));
    1 KB (112 words) - 13:42, 7 July 2020
  • 128 KB (230 words) - 08:13, 11 July 2020
  • <math> \displaystyle F(z)=\frac{1}{2\pi \mathrm i} \oint \frac{F(t)}{t-z} \mathrm d t</math> D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670.
    2 KB (320 words) - 15:14, 21 July 2020
  • z_type Tet2Li3(z_type z){ int n; z_type s,c; c=z-3.*I; c/=4.; s=L4c[90]*c; for(n=89;n>0;n--){ s+=L4c[n]; s*=c;}
    7 KB (724 words) - 14:58, 28 July 2020
  • \(~ T(z)=\exp_2(z)=\exp(\ln(2)z)=2^z \) F(z\!+\!1)=T(F(z))
    6 KB (845 words) - 17:10, 23 August 2020
  • // [[Tet2.cin]] is implementation of z_type Tet2(z_type z) z_type Tet2u(z_type z){ z_type c,e;
    9 KB (699 words) - 20:00, 6 August 2020
  • \(F(z\!+\!1)=\exp\big(\beta F(z)\big)\) Let \(F(z)=L+\varepsilon+O(\varepsilon^2)
    4 KB (548 words) - 14:27, 12 August 2020
  • D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    101 KB (14,846 words) - 00:35, 21 March 2023
  • ...огда Петер дописал 10 раз букву "Z" и 10 раз "z", дети подняли головы и обнаружили, что за Wer zweifelnd noch beim Z bleibt stehn,<br>
    1.18 MB (8,949 words) - 21:24, 7 April 2024
  • ...bitteren Frostes zu erwehren. Das kleine Mädchen mochte kaum fünf Jahre zählen; was aber seine natürliche Gestalt war, konnte man nicht ersehen, de ...wei Tierlein tat. Der Peter verschwand mit seiner Schar. Heidi streichelte zärtlich die eine und dann die andere von den Geißen und sprang um sie heru
    546 KB (98,640 words) - 19:00, 5 April 2024
  • <!-- +7 (926) 352-40-20 z@rotgar.ru !-->
    36 KB (579 words) - 08:25, 16 April 2021
  • for \(m>n\), for any \(z\in \mathcal G\), \OmSum_{j=n}^m f_j ~ (z)= \OmSum_{j=n}^{m-1} f_j ~ (f_m(z))
    2 KB (331 words) - 11:07, 17 May 2021
  • for \(m>n\), for any \(z\in \mathcal G\), \MhSum_{j=n}^m f_j ~ (z)=
    2 KB (355 words) - 11:09, 17 May 2021
  • x0050 [[P]] [[Q]] [[R]] [[S]] [[T]] [[U]] [[V]] [[W]] [[X]] [[Y]] [[Z]] [[[] [[\]] [[]]] [[^]] [[_]]<br> x0070 [[p]] [[q]] [[r]] [[s]] [[t]] [[u]] [[v]] [[w]] [[x]] [[y]] [[z]] [[{]] [[|]] [[}]] [[~]] [[&#x007F;]]<br>
    14 KB (340 words) - 07:38, 30 June 2021
  • ...на территории государства-агрессора. На Z-каналах начались поиски виноватых и обсу 33:13 Мизулина – это Z-гламур
    60 KB (653 words) - 05:14, 9 April 2024
  • ...овершая военные преступления. #потерирф #z #потери ...овершая военные преступления. #потерирф #z #потери
    41 KB (477 words) - 14:27, 27 March 2022
  • \( \exp_b(F(z))=F(z\!+\!1) \)
    10 KB (1,491 words) - 18:09, 11 June 2022
  • ...полец, избивший пенсионера из-за символа Z, отработает 200 часов
    55 KB (619 words) - 10:34, 20 June 2022
  • \(F(z)\) is holomorphic in some strip \( |\Im(z)| < A \)
    3 KB (396 words) - 11:44, 15 August 2022
  • ...ещё одну полоску на машинах, получилось Z.
    522 KB (3,777 words) - 16:52, 9 December 2023
  • 36 KB (452 words) - 10:11, 31 December 2022
  • ...m{sech}(z)=\frac{1}{\cosh(z)}=\frac{2}{\exp(z)+\exp(-z)} =\frac{2}{e^z+e^{-z}} \) \(\displaystyle {\rm sech}(z)=\frac{1}{\cosh(z)}=\frac{2}{e^x+e^{-x}}\)
    3 KB (396 words) - 10:11, 4 April 2023
  • ...м последнее слово состоит из одной буквы Z. Редактор надеется, 13 [[Секретов Прохиндей Фашистович Z]], судья, 404
    21 KB (218 words) - 17:09, 23 June 2023
  • ...-vse-budet-kak-my-lyubim-zhizn-vladlena-tatarskogo-ot-ogrableniya-banka-do-z-geroya/
    53 KB (574 words) - 17:06, 12 September 2023
  • ...всё примерно одно и то же на букву "З" или "Z".
    67 KB (1,022 words) - 18:34, 11 January 2024
  • L\(X\)z\(Y\) , где
    62 KB (1,103 words) - 16:16, 22 February 2024
  • 65 KB (1,542 words) - 22:41, 20 March 2024
  • 37 KB (973 words) - 22:36, 20 March 2024
  • ...изионной и радиовещательной компанией"). Z-фанат обрадовался массированным обстрел
    63 KB (718 words) - 19:03, 19 April 2024
  • ...\Gamma\) refers to [[Gamma function]], \(\Gamma(z)\) \(=\) [[Factorial]]\((z\!-\!1)\) . \mathrm{Student}(\infty,x) = \mathrm{Gau}(x)= \frac{\exp(-z^2/2)}{\sqrt\pi} \)
    12 KB (1,727 words) - 03:21, 11 May 2024

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