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Create the page "Z" on this wiki! See also the search results found.

Page title matches

• Z*e^z
  24 bytes (2 words) - 15:01, 20 June 2013

• File:Z 2d443d04.jpg (1,047 × 1,024 (218 KB)) - 09:40, 21 June 2013

• File:Z 57fe6ee7.jpg (900 × 784 (145 KB)) - 09:41, 21 June 2013

• File:Z ae266144.jpg (900 × 843 (145 KB)) - 09:41, 21 June 2013

• File:Z f8e0e5e5.jpg (900 × 598 (66 KB)) - 09:41, 21 June 2013

• File:Sqrt(exp)(z).jpg (842 × 953 (83 KB)) - 06:14, 1 December 2018

• File:BubnovFront-z-400.jpg (300 × 400 (13 KB)) - 08:31, 1 December 2018

Page text matches

• McCumber relation
  =\exp\!\left( \frac{\hbar \omega_{\rm z}}{k_{\rm B} T}\right)</math> is thermal steady-state ratio of populations; frequency <math>\omega_{\rm z}</math> is called "zero-line" frequency <ref name="comment">
  16 KB (2,521 words) - 15:13, 17 June 2020
• Factorial
  :<math> F(z+1)=(z+1) F(z) </math> for all complex <math>z</math> except negative integer values.
  27 KB (3,925 words) - 18:26, 30 July 2019
• C2011mar16.cc
  main(){ int m,n,k; DB x,y,z, X[49],Y[49], Z[49][17]; char c,d, namae[32]; ...6;k++){ fscanf(i,"%lf",&z); if(z==0) z=1.; printf(" %5.3lf",z); Z[n][k]=z;}
  4 KB (678 words) - 14:24, 20 June 2013
• C2011mar17.cc
  main(){ int m,n,k; DB x,y,z, X[49],Y[49], Z[49][17]; char c,d, namae[32]; ...6;k++){ fscanf(i,"%lf",&z); if(z==0) z=1.; printf(" %5.3lf",z); Z[n][k]=z;}
  5 KB (785 words) - 14:24, 20 June 2013
• Tetration
  : \({\rm tet}_b(z\!+\!1) = \exp_b\!\big( {\rm tet}_b(z) \big)\) ...ast for \(b\!>\!1\), is holomorphic at least in \(\{ z \in \mathbb C : \Re(z)\!>\!-2\}\).
  21 KB (3,175 words) - 23:37, 2 May 2021
• Tetre2215.cc
  // Plot of tetrational \(f={\rm tet}_b(z)\)<br> z_type FIT1(z_type d,z_type z){
  6 KB (1,030 words) - 18:48, 30 July 2019
• Conto.cin
  #define z(m,n) Z[(m)*N1+(n)] #define zmn z(m,n)
  13 KB (2,858 words) - 06:59, 1 December 2018
• Fukushima disaster, timeline of links
  Wang N., Wu X., Kehrwald N., Li Z., Li Q., Jiang X., Pu J. Fukushima nuclear accident recorded in tibetan pla
  146 KB (19,835 words) - 18:25, 30 July 2019
• 4t1c.cc
  main(){ int j,k,m,n; DB x,y,z, p,q, t;
  3 KB (564 words) - 18:33, 28 April 2023
• Mapping
  ...8-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of \(F(z+1)=\exp(F(z))\) in the complex plane.. Mathematics of Computation, 78: 1647-1670. DOI:1 ...cae, v.81, p.65-76 (2011)</ref> is holomorphic solution \(F(z)={\rm tet}_b(z)\) of the equations
  14 KB (2,275 words) - 18:25, 30 July 2019
• Катынь-2
  <ref name="call"> http://thomas.loc.gov/cgi-bin/query/z?c111%3AH.RES.1489%3A Mr.KING. Bill Text 111th Congress (2009-2010) H.RES.14 ...a brzoza nie miała wpływu na pierwotne zniszczenie skrzydła - to jedna z kluczowych konkluzji raportu technicznego podkomisji smoleńskiej.
  145 KB (3,277 words) - 00:40, 25 March 2022
• Katyn-2
  <ref name="call"> http://thomas.loc.gov/cgi-bin/query/z?c111%3AH.RES.1489%3A Mr.KING. Bill Text 111th Congress (2009-2010) H.RES.14 Opracowanie to będzie służyć jako jeden z etapów na drodze do utworzenie tak bardzo potrzebnej międzynarodowej komi
  107 KB (7,830 words) - 15:02, 4 January 2022
• Superfunction
  \(\displaystyle {{F(z)} \atop \,} {= \atop \,} {T^z(t) \atop \,} {= \atop \,}
  25 KB (3,622 words) - 08:35, 3 May 2021
• Natural pentation
  \(\mathrm{pen}(z\!+\!1)=\mathrm{tet}\Big(\mathrm{pen}(z) \Big)\) \(\displaystyle \mathrm{pen}(z)= \sum_{m=0}^{M-1} \alpha_m \mathrm e^{mkz} + O(\mathrm e^{Mkz})\)
  7 KB (1,090 words) - 18:49, 30 July 2019
• Place of science in the human knowledge
  D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
  100 KB (14,715 words) - 16:21, 31 October 2021
• Место науки в человеческом знании
  http://link.springer.com/article/10.1007/s00424-006-0169-z?LI=true#page-1 Marco Piccolino. Luigi Galvani and animal electricity: two c ...ERS/2010superfar.pdf D.Kouznetsov. Solution of F(z+1)=exp(F(z)) in complex z-plane. [[Mathematics of Computation]], <b>78</b>, No.267, p.1647-1670 (2009
  111 KB (2,581 words) - 16:54, 17 June 2020
• Logiu.cin
  // \(T(z)=4 z (1\!-\!z)\) z_type J(z_type z){ return .5-sqrt(.25-z/Q); }
  3 KB (513 words) - 18:48, 30 July 2019
• Square root of factorial
  ...[[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\). ...l}\). It is assumed that \(z\!=\!2\) is [[regular point]] of \(\sqrt{!\,}(z)\), and
  13 KB (1,766 words) - 18:43, 30 July 2019
• Arcfactorial
  : \( \mathrm{Factorial}(\mathrm{ArcFactorial}(z))=z\) However, \(\mathrm{Factorial}^{-1}(z)\) should not be confused with
  3 KB (414 words) - 18:26, 30 July 2019
• Holomorphic extension of the Collatz subsequence
  : \(h(F(z))=F(z\!+\!1)\) : \(h(F(z))-F(z\!+\!1)=0\)
  5 KB (798 words) - 18:25, 30 July 2019
• 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
• Sazae-san constants
  ...{\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
• Acosq
  : \(\mathrm{acosq}(z)=\mathrm{acosc}\left( \mathrm e ^{\mathrm i \pi/4} \,z \right)\) 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
• Acosc.cin
  // 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
• ArcCosqq
  : \(\text{acosqq}(z)=\text{acosq}(z)\, \tan\!\!\big( \text{acosq}(z) \big)\) : \(\text{acosq}(z)=\text{acosq}\big( \mathrm e ^{\mathrm i \pi /4}\, z \big)\)
  2 KB (216 words) - 18:26, 30 July 2019
• Acosc1.cin
  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
• Acosc1
  \(f=\mathrm{Acosc1}(z)\) is solution of equation : \( \displaystyle \mathrm{cosc}(f)=z\)
  6 KB (896 words) - 18:26, 30 July 2019
• ArcFactorial
  : \( \mathrm{Factorial}(\mathrm{ArcFactorial}(z))=z\) However, \(\mathrm{Factorial}^{-1}(z)\) should not be confused with
  3 KB (376 words) - 18:26, 30 July 2019
• Paraxial approximation
  ...\!\!\!\!\!\ (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
• Absorbing Schroedinger
  ...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
• BesselJ0
  J_0''(z)+ J_0'(z)/z+
  6 KB (913 words) - 18:25, 30 July 2019
• ArcSinc
  ...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
• Guiding of waves between absorbing walls
  ...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
• BesselK0
  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
• BesselY0
  solution \(f=f(z)\) of the Bessel equation f''+f'/z+f=0\)
  3 KB (445 words) - 18:26, 30 July 2019
• Cylindric function
  : \(\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ z^2 f''(z) + z f'(z) + (z^2-\nu^2) f(z)=0\) : \(\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ H_\nu(z)=J_\nu(z)+\mathrm i Y_\nu(z)\)
  3 KB (388 words) - 18:26, 30 July 2019
• BesselJ1
  : \(\!\!\!\! \mathrm{BesselJ1}(z)=J_1(z)= \mathrm{BesselJ}[1,z]\) f''(z)+f'(z)/z + (z^2\!-\!1)f(z) = 0\)
  3 KB (439 words) - 18:26, 30 July 2019
• Besselj0.cin
  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
• Besselj1.cin
  // 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
• Bessel function
  \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) 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
• Bessely0.cin
  ...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
  [[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
• Ocean wave solution
  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
• Serega.cin
  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
• Serega function
  ...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
• LogisticSequence
  ...\!\!\!\!\!\!\!\!(1) ~ ~ ~ ~ \mathrm{LogisticOperator}_s(z) = s\,z \,(1\!-\!z)\) where \(z\) is complex number and \(s\) is real number; usually it is assumed that \(
  7 KB (886 words) - 18:26, 30 July 2019
• Efjh.cin
  z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); }
  3 KB (364 words) - 07:00, 1 December 2018
• ArcLogisticSequence
  ...\!\!\!\!\!\! (1) ~ ~ ~ T(z)=\mathrm{LogisticOperator}_s(z)= s\, z\, (1\!-\!z)\) ...~ ~ \mathrm{ArcLogisticSequence}_s(T(z))= \mathrm{ArcLogisticSequence}_s(z)+1\)
  3 KB (380 words) - 18:25, 30 July 2019
• Logistic operator
  ...\!\!\!\!\!\!\!\!(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
• WrightOmega
  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
• Keller function
  ...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
• Shoko function
  :\( \!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ \mathrm {Shoko}(z)=\ln\Big(1+\mathrm e^z (\mathrm e -1) \Big)\) ...!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \mathrm {Shoko}(z)= (\mathrm e -1) \mathrm e^z+ O(\mathrm e^{2z})\)
  10 KB (1,507 words) - 18:25, 30 July 2019
• Shoka function
  :\( \mathrm{Shoka}(z)=z+\ln\!\Big( \exp(-z) +\mathrm e -1\Big)\) ...=\mathrm{Shoka}^{-1}\) can be expressed as elementary function; for \(|\Im(z)| < \pi\),
  3 KB (421 words) - 10:23, 20 July 2020
• ArcShoka
  : \( \displaystyle \mathrm{ArcShoka}(z)= z + \ln\!\left( \frac{\mathrm e^z-1}{\mathrm e-1} \right)\) :\( T(F(z))=F(z\!+\!1)\)
  3 KB (441 words) - 18:26, 30 July 2019
• ArcKeller
  ...\!\!\!\! (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
• Superfactorial.cin
  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
• Facp.cin
  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
• Afacc.cin
  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
• Abelfac.cin
  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
• F45E.cin
  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
• F45L.cin
  z_type f45L(z_type z){ int n; z_type e,s; z-=4.;
  2 KB (163 words) - 18:47, 30 July 2019
• ArcLambertW
  (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
• SuZex
  ...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
• Путаница
  ..., 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
• Tania.cin
  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
• SuZex approximation
  ...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
• SuZexCoef20.cin
  ...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
• SuZex.cin
  ...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
• LambertW.cin
  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
• AuZex.cin
  // 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
• AuZex
  ...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
• Power function
  (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
• Trappmann function
  \(~\mathrm{Tra}(z)=\mathrm e^z +z~\) ...hrm{ArcTra}(z)=\) \(z-\mathrm{Tania}(z\!-\!1)=\) \( z-\mathrm{WrightOmega}(z)\)
  9 KB (1,320 words) - 11:38, 20 July 2020
• Уравнение Шредера для растворимости
  \( \!\!\!(1) ~ ~ ~ T(f(z))=f(kz)\)<br>
  3 KB (47 words) - 18:36, 30 July 2019
• Schroeder equation
  (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
• Fractional iterate
  (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
• Zooming equation
  (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
• Regular iterate
  ...is supposed to be [[fractional iterate]] of function \(T\), id est, for \(z\) in vicinity of point \(L\), (1) \( ~ ~ ~ f^n(z)=T^m(z)\)
  1 KB (178 words) - 06:42, 20 July 2020
• SuTra
  </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
  9 KB (1,285 words) - 18:25, 30 July 2019
• SuFac.cin
  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
• AuFac.cin
  ...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
• ArcTra
  (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
• AuTra
  ...[[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
• AuTra.cin
  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
• F4ten.cin
  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
• Fit1.cin
  ...=\exp(a)\) for \(0.05<a<2\) ; \(\mathrm{tet}_b(z)\) is approximated for \(|z|<1\) using the fruncated Taylor expansion of // \(\mathrm{tet}_b(z) - \ln(z+2)\)
  3 KB (402 words) - 18:48, 30 July 2019
• Logistic
  T(z)=q\cdot z \cdot (1-z) <math> F(z\!+\!1)=T(F(z))
  3 KB (411 words) - 18:26, 30 July 2019
• Цыбко Константин Валерьевич
  http://vk.com/club32160205?z=photo-32160205_304217834%2Fwall-32160205_6475 http://vk.com/club32160205?z=photo-32160205_304216982%2Fwall-32160205_6470
  15 KB (187 words) - 07:36, 1 December 2018
• Sunflower as adsorbent of cesium
  Soudek P, Valenová S, Vavríková Z, Vanek T.
  6 KB (856 words) - 07:06, 1 December 2018

• File:Factorialz.jpg In the complex <math>z</math>-plane, the lines of constant <math>u=\Re(z!)</math> and (1,219 × 927 (479 KB)) - 08:35, 1 December 2018

• File:FactoReal.jpg z_type expauno(z_type z) {int n,m; DB x,y; z_type s; s=expaunoc[24]; x=Re(z);if(x<-.9) return expauno(z+1.)-log(z+1.); (915 × 1,310 (141 KB)) - 08:35, 1 December 2018

• File:OneOverFactorial.jpg Complex map of f(z)=1/z! in the complex z plane. Copy from (1,244 × 949 (276 KB)) - 17:50, 20 June 2013

• File:AbelFacMapT.png $\mathrm{AbalFactorial}(z)=\mathrm{Factorial}^z(3)$ main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,412 × 1,395 (372 KB)) - 17:17, 25 September 2013

• File:AbelFacPloT.png 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;} (1,673 × 1,308 (136 KB)) - 09:43, 21 June 2013

• File:AbelFactorialMap.png int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (675 × 673 (120 KB)) - 08:28, 1 December 2018

• File:AbelFactorialR.png :$G(z!)=G(z)+1$ (1,060 × 705 (34 KB)) - 09:39, 21 June 2013

• File:AciplotTa.png z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;} (1,267 × 1,267 (84 KB)) - 09:41, 21 June 2013

• File:AcipmapTjpg.jpg z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;} (1,759 × 1,746 (661 KB)) - 09:41, 21 June 2013

• File:AcipmapTpng.png z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;} (844 × 838 (199 KB)) - 09:41, 21 June 2013

• File:AcomapT200.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (2,345 × 2,328 (1.06 MB)) - 09:41, 21 June 2013

• File:Acosc1mapT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,759 × 1,746 (862 KB)) - 09:41, 21 June 2013

• File:Acosc1plotT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; /* M(Tarao,Sazae) DO(m,200){x=-.33+.01*(m+.5); z=x; DB t=x-Tarao0, u=sqrt(t); (851 × 2,728 (203 KB)) - 09:41, 21 June 2013

• File:AcoscmapT300.png z_type cosc(z_type z) {return cos(z)/z;} z_type cosp(z_type z) {return (-sin(z) - cos(z)/z)/z ;} (3,517 × 3,492 (1.64 MB)) - 09:41, 21 June 2013

• File:AcoscplotT.png : $\displaystyle \mathrm{Left}_3(z)=\mathrm{Sazae} \frac{2(z-\mathrm{Tarao})} (1,267 × 1,267 (152 KB)) - 09:41, 21 June 2013

• File:AcosmapT200.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (1,773 × 1,752 (797 KB)) - 09:41, 21 June 2013

• File:AcosplotT.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (897 × 1,387 (69 KB)) - 09:41, 21 June 2013

• File:Acosq1plotT.png $\mathrm{acosq}_1(z)=\mathrm{acosc}_1\left( \mathrm e ^{ \mathrm i \pi/4 } z \right)$ :\mathrm{expan}_1(z)=\frac{3 \pi}{2} (2,512 × 3,504 (379 KB)) - 09:41, 21 June 2013

• File:AcosqplotT100.png :$ \mathrm{acosq}(z)=\mathrm{acosc}\left( \mathrm e^{\mathrm i \pi/4}\, z\right)$ for real values of $z$. (2,231 × 1,215 (152 KB)) - 09:41, 21 June 2013

• File:AcosqqplotT.png : $\text{acosqq}(z)=\text{acosq}(z)\, \tan\!\!\big( \text{acosq}(z) \big)$ : $\text{acosq}(z)=\text{acosq}\big( \mathrm e ^{\mathrm i \pi /4}\, z \big)$ (1,686 × 1,823 (148 KB)) - 09:41, 21 June 2013

• File:AfacmapT800.png 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); (2,355 × 2,334 (1.03 MB)) - 09:41, 21 June 2013

• File:AfacplotT2px300.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,534 × 1,267 (141 KB)) - 09:41, 21 June 2013

• File:ArcCipMapT.jpg z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;} (1,759 × 1,746 (661 KB)) - 09:41, 21 June 2013

• File:ArcKellerMapT.png ...left( \frac{1}{\mathrm e}+\frac{\mathrm e \!-\!1}{\mathrm e}\, \mathrm e^{-z} \right)$ // z_type Shoko(z_type z) { return log(1.+exp(z)*(M_E-1.)); } (1,773 × 1,752 (924 KB)) - 08:29, 1 December 2018

• File:ArcSeregaMapT.png : $ \mathrm {Serega}(z)=z+\mathrm i \exp( \mathrm i ~ z^*)$ // z_type Serega(z_type z); (1,312 × 1,312 (483 KB)) - 09:43, 21 June 2013

• File:ArcShokaMapT.png z_type Shoko(z_type z){ return log(1.+exp(z)*(M_E-1.)); } z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } (1,773 × 1,752 (1,010 KB)) - 08:29, 1 December 2018

• File:ArcTaniaMap.png :$ \mathrm{ArcTania}(z)= z+\ln(z) -1$ z_type ArcTania(z_type z) {return z + log(z) - 1. ;} (851 × 841 (626 KB)) - 08:30, 1 December 2018

• File:ArcTraMapT.jpg //z_type zex(z_type z){ return z*exp(z);} //z_type tra(z_type z){ return z+exp(z);} (2,576 × 2,559 (1.31 MB)) - 08:30, 1 December 2018

• File:AsimapT.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (1,759 × 1,746 (746 KB)) - 09:41, 21 June 2013

• File:AsincmapT.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (1,759 × 1,746 (896 KB)) - 09:41, 21 June 2013

• File:AsincplotT500.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (843 × 2,014 (184 KB)) - 09:41, 21 June 2013

• File:AsinplotT.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (897 × 1,381 (70 KB)) - 09:41, 21 June 2013

• File:AuTraMapT.jpg ...l function]] of the [[Trappmann function]] $\mathrm{tra}(z)\!=\!z\!+\!\exp(z)$. z_type arctra(z_type z){return z-Tania(z-1.);} (4,367 × 4,317 (1.82 MB)) - 08:30, 1 December 2018

• File:AuTraPlotT.jpg $ \mathrm{tra}(z)=z+\exp(z)$ z_type tra(z_type z){ return exp(z)+z;} (1,678 × 1,262 (172 KB)) - 08:30, 1 December 2018

• File:AuZexLamPlotT.jpg main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("AuZexLam.eps","w"); ado(o,1204,404); (2,508 × 841 (169 KB)) - 08:30, 1 December 2018

• File:AuZexMapT.jpg // z_type zex(z_type z) { return z*exp(z) ; } z_type LambertWo(z_type z){ int n,m=48; z_type d=-z; (4,367 × 4,326 (1.53 MB)) - 08:30, 1 December 2018

• File:B271a.png D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. <!-- :$ \mathrm{ate}(\exp(z))=\mathrm{ate}(z)\!+\!1~,$ (1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018

• File:B271t.png 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); if(abs(z+2.)>.04) (1,609 × 1,417 (791 KB)) - 08:30, 1 December 2018

• File:B271t3T.png 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); //if(abs(z+2.)>.019) (1,742 × 1,726 (1,007 KB)) - 08:30, 1 December 2018

• File:BesselH0mapT050.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,420 × 721 (966 KB)) - 09:42, 21 June 2013

• File:Besselh0mapT100.png : $H_0(z)=J_0(z)+\mathrm i Y_0(z)$ main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,284 × 1,164 (1.65 MB)) - 08:31, 1 December 2018

• File:Besselj0j1plotT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (3,405 × 484 (112 KB)) - 09:42, 21 June 2013

• File:Besselj0map1T080.png 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;} (1,827 × 932 (1.7 MB)) - 09:41, 21 June 2013

• File:Besselj0mapT100.png 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;} (1,173 × 1,164 (1.45 MB)) - 09:41, 21 June 2013

• File:Besselj1mapT080.png // BesselJ[1,z] implementation: z_type BesselJ1o(z_type z){ int n; z_type c,s,t; (2,056 × 1,048 (1.72 MB)) - 09:42, 21 June 2013

• File:Besselk0mapT900.png z_type besselk0o(z_type z){ z_type L=log(z); z_type t=z*z; z_type besselk0O(z_type z){ z_type t=1./z, q=sqrt(t); z_type s; (2,118 × 2,105 (1.62 MB)) - 09:41, 21 June 2013

• File:BesselY0J0J1plotT060.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,362 × 217 (47 KB)) - 09:42, 21 June 2013

• File:BesselY0mapWideT039.png ...tion]] of zero order, id est, the [[BesselY0]]; $Y_0(z)=\mathrm{BesselY}[0,z]$ the expansion at small values of $|z|$ and the expansion for the large values. (See the implementation at [[Bess (2,191 × 563 (1.91 MB)) - 09:42, 21 June 2013

• File:CihplotT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; //z=x; y=Re(ACip5(z)); (1,267 × 1,059 (87 KB)) - 09:41, 21 June 2013

• File:CipmapT.jpg [[Complex map]] of function $\mathrm{Cip}(z)=\cos(z)/z$. main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,759 × 1,746 (1.58 MB)) - 08:32, 1 December 2018

• File:CipmapT.png [[Complex map]] of function $\mathrm{Cip}(z)=\cos(z)/z$. main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (844 × 838 (484 KB)) - 09:41, 21 June 2013

• File:CoscmapT100.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,284 × 1,164 (1.75 MB)) - 09:41, 21 June 2013

• File:CoshcmapT120.png z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} (1,407 × 1,397 (1.47 MB)) - 09:41, 21 June 2013

• File:CoshcplotT.png : $\displaystyle \mathrm{coshc}(z)=\frac{\cosh(z)}{z}$ : $\cosh(z)=(\mathrm e^z+\mathrm e^{-z})/2$ (465 × 851 (36 KB)) - 09:41, 21 June 2013

• File:Doya10map4bT60.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (714 × 700 (342 KB)) - 08:34, 1 December 2018

• File:Doya20map4bT100.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,190 × 1,167 (663 KB)) - 08:34, 1 December 2018

• File:Doya500.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(y,x); (153 × 237 (55 KB)) - 00:19, 14 July 2020

• File:DoyaconT70.png z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;} (442 × 817 (98 KB)) - 09:39, 21 June 2013

• File:Doyam10map4bT100.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,199 × 1,167 (629 KB)) - 09:39, 21 June 2013

• File:DoyaPlotT100.png $ \mathrm{Doya}_t(z)=\mathrm{Tania}(t+\mathrm{ArcTania}(z))$ $\displaystyle \mathrm{Tania}'(z)= (580 × 590 (77 KB)) - 08:34, 1 December 2018

• File:DoyaplotTc.png main(){ int j,k,m,n; DB x,y,t,e, a; z_type z; M(0,0); for(n=1;n<151;n++){x=.02*n;z=x;y=Re(Doya(1.,z)); L(x,y)} (881 × 1,325 (95 KB)) - 09:43, 21 June 2013

• File:E1efig09abc1a150.png 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); (2,234 × 711 (883 KB)) - 08:34, 1 December 2018

• File:Elutin1a4tori.jpg F[c_, z_] = 1/2 (1 - Cos[2^c ArcCos[1 - 2 z]]) : $f^c(z)=F(c+G(z))$ (922 × 914 (62 KB)) - 09:38, 21 June 2013

• File:Esqrt2iterMapT.png $T(x) = \Big(\sqrt{2}\Big){^z}= \exp_b(z)$ $T^{1/3}(z)=F\!\left(\frac{1}{3}+G(z)\right)$ (1,092 × 1,080 (1.36 MB)) - 09:43, 21 June 2013

• File:Expc.jpg <math>\exp^c(z)=\mathrm{tet}\Big(c+\mathrm{tet}^{-1}(z)\Big)</math> (941 × 852 (48 KB)) - 18:39, 11 July 2013

• File:ExpIte4T.jpg // z_type tra(z_type z){ return exp(z)+z;} // z_type F(z_type z){ return log(suzex(z));} (1,673 × 1,673 (901 KB)) - 08:35, 1 December 2018

• File:ExpMapT.png 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); //if(abs(z+2.)>.019) (1,742 × 1,726 (1.62 MB)) - 08:35, 1 December 2018

• File:ExpQ2mapT.png main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,765 × 1,729 (1.15 MB)) - 08:35, 1 December 2018

• File:FacIteT.jpg //DB F(DB z) { return exp( exp( log(B)*z));} //DB G(DB z) { return log( log(z) )/log(B);} (2,093 × 2,093 (795 KB)) - 08:35, 1 December 2018

• File:FacmapT500.png 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); (2,355 × 2,334 (1.73 MB)) - 09:41, 21 June 2013

• File:Filogbigmap100.png ...og}(z)$ expresses the [[fixed point]] of [[logarithm]] to base $b\!=\!\exp(z)$. $\mathrm{Filog}(z^*)^*$ (2,870 × 2,851 (847 KB)) - 08:36, 1 December 2018

• File:Filogmap300.png ...og}(z)$ expresses the [[fixed point]] of [[logarithm]] to base $b\!=\!\exp(z)$. $\mathrm{Filog}(z^*)^*$ (893 × 897 (292 KB)) - 09:40, 21 June 2013

• File:FilogmT1000a.jpg \( z=\mathrm{Filog}(a)~\) expresses solution \(z\) of equation \(\ln(z)/a=z\). int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (4,359 × 2,989 (1.68 MB)) - 03:45, 21 July 2020

• File:Hades500.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(y,x); (153 × 237 (55 KB)) - 09:39, 21 June 2013

• File:IterEq2plotU.png DB F(DB z) { return exp( exp( log(B)*z));} DB G(DB z) { return log( log(z) )/log(B);} (2,944 × 2,944 (986 KB)) - 21:42, 27 September 2013

• File:IterPowPlotT.png ...c function, id est, [[power function]] for power 2; $y=\mathrm{Pow}_2^{~c}(z)=T^c(x)~$ for various values of number $c$ of iteration. Here, : $\!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$ (2,093 × 2,093 (680 KB)) - 20:50, 28 September 2013

• File:KellerDoyaT.png z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;} (661 × 881 (70 KB)) - 08:39, 1 December 2018

• File:KellerMapT.png $\mathrm{Keller}(z)=z+\ln\!\Big(\mathrm e-(\mathrm e\!-\!1) \mathrm e^{-z}\Big)$. z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } (1,773 × 1,752 (1 MB)) - 08:39, 1 December 2018

• File:KellerPlotT.png z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;} (870 × 885 (118 KB)) - 08:39, 1 December 2018

• File:LambertWmap150.png z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;} (1,773 × 1,752 (523 KB)) - 08:41, 1 December 2018

• File:LambertWplotT.png #define Re(z) z.real() #define Im(z) z.imag() (1,267 × 839 (81 KB)) - 09:43, 21 June 2013

• File:Logi1a345T300.png $ \mathrm{LogisticPoerator}_s^{\,c}(z)= \mathrm{LogisticSequence}_s\Big( c + \mathrm{ArcLogisticSequence}(z) \big)$ (1,636 × 565 (184 KB)) - 08:41, 1 December 2018

• File:Logi2c3T1000.png z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); } (1,772 × 1,758 (1.36 MB)) - 08:41, 1 December 2018

• File:Logi2c4T1000.png z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); } (1,772 × 1,758 (1.39 MB)) - 08:41, 1 December 2018

• File:Logi2d3T1500.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,657 × 2,657 (1.47 MB)) - 08:41, 1 December 2018

• File:Logi5T1500.png int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (3,404 × 540 (185 KB)) - 06:28, 10 June 2022

• File:Logi5U1500.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (3,404 × 955 (403 KB)) - 06:30, 10 June 2022

• File:LogiarcT300.png main(){ int j,k,m,n; DB x0,y0,x,y, p,q, t; z_type z,c,d; DO(m,1250) { x=x0-.001*m; z=E(x); y=Re(z); L(x,y); if( y<-2.01) break; } (598 × 1,287 (90 KB)) - 09:43, 21 June 2013

• File:LogQ2mapT2.png main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,765 × 1,729 (1.43 MB)) - 09:43, 21 June 2013

• File:MicroChipAtomicTrap00.jpg ...ield is realized at the side of the chip, close to the central part of the z-electrode with electric current. The movement of atoms along the wire is limited by the angles of the "Z". Additional electrodes were designed to play with the effective potential (890 × 976 (44 KB)) - 09:39, 21 June 2013

• File:Modeab02T.png z_type acosq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c;} z_type acosqq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c*tan(c);} (1,678 × 519 (66 KB)) - 09:41, 21 June 2013

• File:Modeab25T.png z_type acosq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c;} z_type acosqq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c*tan(c);} (1,678 × 519 (76 KB)) - 09:41, 21 June 2013

• File:Modeabso25T.png z_type acosq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c;} z_type acosqq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c*tan(c);} (2,657 × 905 (262 KB)) - 09:41, 21 June 2013

• File:ObamaPutin.jpg ...kolí? No ano, hlavně USA. Jak nejefektivněji dosáhnou USA toho, že se z Ruska stane slabá země? Správně, dosadí na nejvyšší post svého age (488 × 634 (111 KB)) - 08:45, 1 December 2018

• File:PowIteT.jpg ...c function, id est, [[power function]] for power 2; $y=\mathrm{Pow}_2^{~c}(z)=T^c(x)~$ for various values of number $c$ of iteration. Here, : $\!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$ (2,093 × 2,093 (1.01 MB)) - 08:46, 1 December 2018

• File:PowPloT.jpg //DB F(DB z) { return exp( exp( log(B)*z));} //DB G(DB z) { return log( log(z) )/log(B);} (2,097 × 2,097 (697 KB)) - 09:44, 21 June 2013

• File:QFacMapT.png $f(z)=\mathrm{Factorial}^{1/2}(z)$ $f(z)= \mathrm{SuperFactorial}\Big(0.5+\mathrm{AbelFactorial}(z)\Big)$ (1,412 × 1,395 (1.47 MB)) - 09:43, 21 June 2013

• File:QFactorialQexp.jpg : <math> H\big(S(z)\big)=S(z\!+\!1)</math> : <math> H^c(z)=S(c+S^{-1}(z))</math> (800 × 399 (121 KB)) - 17:23, 11 July 2013

• File:SazaeconT.png ...=\frac{\cos(z)}{z} ~,$ $~ ~ \displaystyle \mathrm{cohc}(z)=\frac{\cosh(z)}{z} ~,$ main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,118 × 1,682 (216 KB)) - 09:41, 21 June 2013

• File:SeregaFunction03.png main(){ int n; DB x,y,t,c,s,z; FILE *o; DO(n,1260){t=-3.04+.005*n; c=cos(t); s=sin(t); z=1.3-c; z*=z; (2,509 × 434 (51 KB)) - 08:51, 1 December 2018

• File:Sfaczoo300.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,142 × 453 (302 KB)) - 00:12, 29 February 2024

• File:ShokaMapT.png ...]] of the [[Shoka function]], $\mathrm{Shoka}(z)=z-\ln\!\Big( \mathrm e^{-z} +\mathrm e -1 \Big)$ : ...that of the [[Shoko function]], $\mathrm{Shoko}(z)=\ln\!\Big(1+ \mathrm e^z (\mathrm e \!-\! 1) \Big)$ (1,773 × 1,752 (992 KB)) - 08:51, 1 December 2018

• File:ShokoMapT.png z_type Shoko(z_type z) { return log(1.+exp(z)*(M_E-1.)); } main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; (1,773 × 1,752 (964 KB)) - 09:43, 21 June 2013

• File:SimudoyaTb.png :$T(z)=\mathrm{Doya}_1(z)=\mathrm{LambertW}\Big( z~ \mathrm{e}^{z+1} \Big)$ main(){ int j,k,m,n; DB x,y,t,e, a; z_type z; (3,388 × 1,744 (537 KB)) - 08:51, 1 December 2018

• File:SincmapT100.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,284 × 1,164 (1.63 MB)) - 09:41, 21 June 2013

• File:SincplotT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (3,350 × 1,001 (221 KB)) - 09:41, 21 June 2013

• File:SqrtExpZ.jpg [[Complex map]]s of function <math>f=\exp^c(z)</math> in the <math>z</math> plane D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. (842 × 953 (83 KB)) - 11:56, 21 June 2013

• File:Sqrt2figf45bT.png :$ \displaystyle \tilde f(z)= \sum_{n=0}^{N-1} a_n \exp(knz)$ $T(z)=\exp_{\sqrt{2}}(z)=\Big( \sqrt{2} \Big)^z$ (2,180 × 2,159 (1.01 MB)) - 08:52, 1 December 2018

• File:Sqrt2figf45eT.png z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161)); (2,180 × 2,159 (1.18 MB)) - 08:52, 1 December 2018

• File:Sqrt2figL45eT.png z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161)); (2,180 × 2,159 (1.07 MB)) - 12:53, 20 July 2020

• File:SuperFacMapT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,412 × 1,395 (457 KB)) - 09:43, 21 June 2013

• File:SuperFacPlotT.png : $\mathrm{Factorial}(z\!+\!1)=(z\!+\!1)\, \mathrm{Factorial}(z)~$, $~\mathrm{Factorial}(0)\!=\!1$ [[SuperFactorial]]$(z)=\mathrm{Factorial}^z(3)$ is holomorphic solution of equations (1,673 × 2,109 (181 KB)) - 09:43, 21 June 2013

• File:Superfactocomple1.png int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (706 × 706 (172 KB)) - 00:10, 29 February 2024

• File:Superfactorea500.png : \(\mathrm{Factorial}(z)=z \times \mathrm{Factorial}(z\!-\!1) ~ \forall z\in \mathbb C \backslash \{ -n, n\in \mathbb N \} \) : \( \mathrm{Factorial}(z^*)=\mathrm{Factorial}(z)^* \) (575 × 748 (50 KB)) - 00:06, 29 February 2024

• File:SuperFacZoomT.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,304 × 930 (1,016 KB)) - 09:43, 21 June 2013

• File:SuTraMapT.jpg $\mathrm{Tra}(z)\!=\!z\!+\!\exp(z)$. In the figure, z_type tra(z_type z) {return z+exp(z);} (4,176 × 4,176 (1.76 MB)) - 08:53, 1 December 2018

• File:SuTraPlo3T.jpg $\mathrm{Tra}(z)\!=z\!+\!\exp(z)$. z_type tra(z_type z){ return exp(z)+z;} (1,262 × 1,694 (182 KB)) - 08:53, 1 December 2018

• File:SuZex0map48small.png $\displaystyle \mathrm{SuZex}(z) \approx P_{48}(z)=\sum_{n=0}^{48} \,c_n\, z^n$ ...ansfer equation]] $\mathrm{SuZex}(z\!+\!1)=\mathrm{zex}\Big(\mathrm{SuZex}(z)\Big)$ are used; <br> (1,230 × 1,230 (734 KB)) - 09:43, 21 June 2013

• File:SuZexD1mapT.png ...ex]], which is entire [[superfunction]] of [[Zex]], $\mathrm{zex}(z)=z\exp(z)$. ...= \frac{-1}{z} +\frac{ \ln(-z)}{2 z^2}+ \frac{-.05\ln(-z)^2-.02\ln(-z)-.4}{z^3}$ (2,576 × 2,559 (1.04 MB)) - 08:53, 1 December 2018

• File:SuZexMapT.jpg [[Complex map]] of function [[SuZex]], superfunction of [[zex]]$(z)~=z\,\exp(z)$. $u\!+\!\mathrm i v= \mathrm{SuZex}(z\!+\!\mathrm i y)$. (4,576 × 4,542 (1.77 MB)) - 09:43, 21 June 2013

• File:SuZexo20testTjpg.jpg z_type zex(z_type z) { return z*exp(z);} z_type suzexo(z_type z){ int n,m; z_type L=log(-z); z_type c[21]; z_type s; (4,576 × 4,542 (1.81 MB)) - 17:14, 25 September 2013

• File:SuZexoMapJPG.jpg ...playstyle \mathrm{SuZex}(z-x_1)\approx Q_N(z)=\frac{1}{z} ~\sum_{n=0}^{N}~ z^{-n}~ \sum_{m=0}^n ~ a_{n,m} \ell^m$ where $\ell=\ln(-z)$. (4,576 × 4,542 (1.73 MB)) - 17:15, 25 September 2013

• File:SuZexPlot511T.jpg ...n [[SuZex]] in comparison to its transfer function [[zex]]$(z)\!=\!z\,\exp(z)$: z_type zex(z_type z) { return z*exp(z);} (1,055 × 2,292 (188 KB)) - 08:53, 1 December 2018

• File:SuZexTay0testT.png $\displaystyle \mathrm{SuZex}(z) \approx P_{48}(z)=\sum_{n=0}^{48} \,c_n\, z^n$ $\displaystyle A_{48}(z)= -\lg \left( \frac (1,230 × 1,230 (354 KB)) - 09:43, 21 June 2013

• File:SuZexTay2008deviTjpg.jpg ...is [[superfunction]] for the [[transfer function]] T(z)=[[zex]](z)= x exp(z) z_type zex(z_type z) { return z*exp(z);} (4,576 × 4,542 (1.93 MB)) - 17:14, 25 September 2013

• File:SuZexTay2008t12MapT.jpg ...is [[superfunction]] for the [[transfer function]] T(z)=[[zex]](z)= x exp(z) z_type zex(z_type z) { return z*exp(z);} (4,576 × 4,542 (1.71 MB)) - 09:43, 21 June 2013

• File:TaniaBigMap.png $f=\mathrm{Tania}(z)=$ $ (z\!+\!1)\!-\!\ln(z\!+\!1) +\frac{ \ln(z\!+\!1)}{z+1}$ $ (851 × 841 (654 KB)) - 08:53, 1 December 2018

• File:TaniaContourPlot100.png z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;} (1,182 × 1,168 (931 KB)) - 08:53, 1 December 2018

• File:TaniaNegMapT.png For $|\Im(z)| < \pi$, $\Re(z)\rightarrow - \infty$, :$ \mathrm{Tania}(z) ~ \sim ~ (1,773 × 1,752 (306 KB)) - 09:39, 21 June 2013

• File:TaniaPlot.png : $ \displaystyle f'(z)= \frac{f(z)}{1+f(z)}$ (807 × 424 (16 KB)) - 09:39, 21 June 2013

• File:TaniaSinguMapT.png : where $t= \sqrt{\frac{2}{9}(z+2-\mathrm{i})}$ is shown in the $x\!=\!\Re(z)$, $y\!=\!\Im(z)$ plane with<br> (851 × 841 (615 KB)) - 08:53, 1 December 2018

• File:TaniaTaylor0T.png +\frac{z}{2}$ $ +\frac{z^2}{16}$ $ (851 × 841 (650 KB)) - 09:39, 21 June 2013

• File:Tet10bxr.jpg int main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d; ...25){\sx{.7}{$y\!=\!{\rm tet}_{b}(x)$ ~as solution of~ $F(z\!+\!1)=\exp_b(F(z))$ ~,~ $F(0)\!=\!1$}} (2,491 × 1,952 (236 KB)) - 08:53, 1 December 2018

• File:Tet10bxr.png $y=\mathrm{tet}_b(x)~$ versus $z$ for various values of $b$. int main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d; (1,196 × 936 (120 KB)) - 08:53, 1 December 2018

• File:TetPlotU.png main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (838 × 2,088 (124 KB)) - 08:53, 1 December 2018

• File:Tetreal10bx10d.png main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d; ...25){\sx{.7}{$y\!=\!{\rm tet}_{b}(x)$ ~as solution of~ $F(z\!+\!1)=\exp_b(F(z))$ ~,~ $F(0)\!=\!1$}}% <br> (2,192 × 2,026 (436 KB)) - 13:56, 5 August 2020

• File:Tetreal2215.jpg // Plot of tetrational $f={\rm te}_{\ln(b)}(z)=tet_b(z) <br> z_type FIT1(z_type d,z_type z){ (876 × 881 (130 KB)) - 09:38, 21 June 2013

• File:TetSheldonImaT.png \exp(a F(z))=F(z\!+\! 1)$ K(z)= (4,359 × 980 (598 KB)) - 09:40, 21 June 2013

• File:Tetsheldonmap03.png z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd; z+=z_type(0.1196573712872846, 0.1299776198056910); (2,549 × 702 (982 KB)) - 08:53, 1 December 2018

• File:TetSheldonTestImaT.png $\mathrm{tet}_s(z)$ along lines $z=\pm 1/2 + \mathrm i y$ versus $y$. (4,318 × 980 (322 KB)) - 08:53, 1 December 2018

• File:TraItT.jpg z_type tra(z_type z){ return exp(z)+z;} z_type F(z_type z){ return log(suzex(z));} (1,258 × 1,258 (604 KB)) - 08:54, 1 December 2018

• File:TraItu3T.jpg z_type tra(z_type z){ return exp(z)+z;} z_type F(z_type z){ return log(suzex(z));} (1,258 × 1,258 (346 KB)) - 09:44, 21 June 2013

• File:TraMapT.jpg [[Complex map]] of the [[Trappmann function]] $\mathrm{tra}(z)=z+\mathrm e^z$. //z_type zex(z_type z){ return z*exp(z);} (2,576 × 2,559 (1.75 MB)) - 08:54, 1 December 2018

• File:ZexD6mapT100.png $ \mathrm{zex}(z)=z\exp(z)$ z_type zex(z_type z){ return z*exp(z);} (1,717 × 1,706 (1.66 MB)) - 08:57, 1 December 2018

• File:ZexIteT.jpg for various number $n$ of iterates. Here, $\mathrm{zex}(z)\!=\!z\exp(z)$. The non-integer iterates are implemented through the [[superfunction]] o main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("ZexIte.eps","w"); ado(o,1204,1204); (2,508 × 2,508 (973 KB)) - 10:31, 20 July 2020

• Revizor3
  ...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
• Ревизор2012
  ...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
• Maps of tetration
  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.
  5 KB (761 words) - 12:00, 21 July 2020
• GSL
  <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
• Abelpower
  ...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
• Algebra of generalized functions
  \lim_{z\rightarrow 0}~ \Big( \theta(x\!+\!y\!+\!z)-\theta(x\!-\!y\!-\!z) \Big)
  38 KB (6,232 words) - 18:46, 30 July 2019
• Aunemco.txt
  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
• Nori
  ...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
• Putin world war
  ...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
  148 KB (18,467 words) - 18:50, 13 January 2022
• Superlogarithm
  \(f(z+1)=\ln(f(z))\) \(f(z)=\mathrm{tet}(-z)\)
  1 KB (173 words) - 19:31, 30 July 2019
• Superpower
  ...'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
• Susin.cin
  ...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
• Sutran.cin
  ...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
• Интегральная формула Коши
  <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.
  16 KB (821 words) - 14:42, 21 July 2020
• Julia set
  \(\mathbb J(f) = \{ z \in C : \exists ~ n\in \mathbb N_+ ~:~ f^n(z) \bar \in C\}\) \(\mathbb F(f) = \{ z \in C : \forall ~ n\in \mathbb N_+ ~,~ f^n(z) \in C\}\)
  4 KB (630 words) - 18:44, 30 July 2019

• File:QfacMapT500a.jpg is such function that $ h(h(z)) = z!$ in wide range of values of $z$. Levels $u=\Re(h(z))=\rm const$ and (2,352 × 2,352 (1.99 MB)) - 16:44, 11 July 2013

• Superfac.cin
  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
• Arcsuperfac.cin
  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

• File:QexpMapT400.jpg int main(){ int j,k,m,n,n1; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,881 × 1,881 (1.83 MB)) - 18:26, 11 July 2013

• Conjugation
  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
• Mathematical notations
  ...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
• Mandelbrot polynomial
  \( P_c(z)=z^2+c\) \(\Phi(z)=p(F(z))\)
  2 KB (229 words) - 18:44, 30 July 2019

• File:Exp1mapT200.jpg $u+\mathrm i v = \mathrm{tet}(1.+\mathrm{ate}(z))=\exp(z)$ in the $z=x+\mathrm i y$ plane. (2,281 × 1,179 (1.14 MB)) - 12:37, 28 July 2013

• File:Exp09mapT200.jpg 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); //if(abs(z+2.)>.019) (2,281 × 1,179 (1.23 MB)) - 12:28, 28 July 2013

• Iterate of exponential
  ...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:Exp05mapT200.jpg 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); //if(abs(z+2.)>.019) (1,711 × 885 (872 KB)) - 12:20, 28 July 2013

• File:Exp01mapT200.jpg 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); //if(abs(z+2.)>.019) (2,281 × 1,179 (895 KB)) - 12:04, 28 July 2013

• File:Exm01mapT200.jpg 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); //if(abs(z+2.)>.019) (2,281 × 1,179 (834 KB)) - 12:52, 28 July 2013

• File:Exm05mapT200.jpg 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); //if(abs(z+2.)>.019) (2,281 × 1,179 (705 KB)) - 12:54, 28 July 2013

• File:Exm09mapT200.jpg 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); //if(abs(z+2.)>.019) (2,281 × 1,179 (560 KB)) - 12:56, 28 July 2013

• File:Exm1mapT200.jpg 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); //if(abs(z+2.)>.019) (2,281 × 1,179 (544 KB)) - 12:47, 28 July 2013

• Category:Iteration of exp
  $\exp^n(z)=\mathrm{tet}(n+\mathrm{ate}(z))$
  10 members (0 subcategories, 9 files) - 13:04, 28 July 2013
• Iterate of linear fraction
  [[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 \(n\)
  13 KB (2,088 words) - 06:43, 20 July 2020

• File:Fracit20t150.jpg $\displaystyle f(z)=\frac{x}{c+z}$ at $c\!=\!2$. f^n(z)=\frac{z}{c^n+\frac{1-c^n}{1-c} z}$ (1,466 × 1,466 (463 KB)) - 08:36, 1 December 2018

• File:Fracit10t150.jpg $\displaystyle f(z)=\frac{x}{c+z}$ at $c\!=\!1$. f^n(z)=\frac{z}{c^n+\frac{1-c^n}{1-c} z}$ (1,466 × 1,466 (564 KB)) - 08:36, 1 December 2018

• File:Fracit05t150.jpg $\displaystyle f(z)=\frac{x}{c+z}$ at $c\!=\!0.5$. f^n(z)=\frac{z}{c^n+\frac{1-c^n}{1-c} z}$ (1,466 × 1,466 (441 KB)) - 08:36, 1 December 2018

• File:Frac1zt.jpg [[Iterate]]s of function $T(z)=-1/z$ $\displaystyle F(z)=\tan\left(\frac{2}{\pi} z\right)$ (2,089 × 2,089 (734 KB)) - 08:36, 1 December 2018

• File:Frac2zt.jpg [[Iteration]] of function $T(z)=-4/z$. (2,089 × 2,089 (716 KB)) - 21:47, 29 August 2013

• Linear fraction
  \((1) ~ ~ ~ \displaystyle T(z)=\frac{u+v z}{w+z}\) \((2) ~ ~ ~ \displaystyle A+B z= \lim_{M\rightarrow \infty} \frac{M A+ M B}{M+z}\)
  5 KB (830 words) - 18:44, 30 July 2019
• Superfunctions
  \(T(F(z))=F(z+1)\) \(G(T(z))=G(z)+1\)
  15 KB (2,166 words) - 20:33, 16 July 2023
• Linear fuction
  [[File:Itelin125T.jpg|440px|thumb|Iterates of \(T(z)=A+Bz~\) at \(~A\!=\!1\), \(B\!=\!2~\); \(~y=T^n(x)~\) versus \(x\) for var \((1) ~ ~ ~ T(z)=A+B z\)
  2 KB (234 words) - 18:43, 30 July 2019
• Morias
  \(\mathrm{mori}(z)=\displaystyle \frac{ J_0 (L_1 z)}{1-z^2}\) For integer \(m>0\) and \(|z|\gg 1\), function [[mori]]\((z)\) can be approximated with
  3 KB (456 words) - 18:44, 30 July 2019

• File:Itelin125T.jpg $T(z)=A+B z$ (2,088 × 2,088 (893 KB)) - 08:38, 1 December 2018

• File:Fz2z1mapT.jpg $\displaystyle f(z)=\frac{1}{2^z-2}$ z_type F(z_type z) {return (c-1.)/(pow(2.,z)-c);} (4,175 × 4,175 (1.57 MB)) - 08:36, 1 December 2018

• File:Gz2z1mapT.jpg $g(z)=\log_2(1+1/z)$ z_type F(z_type z) {return (c-1.)/(pow(c,z)-c);} (4,175 × 4,175 (1.67 MB)) - 08:37, 1 December 2018

• File:F1xmapT.jpg [[complex map]] of function $f(z)=-1/z$; $u+\mathrm i y=f(z+\mathrm i y)$ (4,175 × 4,175 (1.63 MB)) - 08:35, 1 December 2018

• File:Z2itmapT.jpg [[Complex map]] of function $T(z)=z^2$. // z_type F(z_type z) {return (c-1.)/(pow(2.,z)-c);} (2,175 × 2,158 (1.74 MB)) - 08:57, 1 December 2018

• File:AbelFacMapT.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (4,704 × 4,649 (1.81 MB)) - 08:28, 1 December 2018

• File:FacitT.jpg int main(){ int m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,2001){x=.004*n; z=x; c=fac(z); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W (2,092 × 2,092 (891 KB)) - 08:35, 1 December 2018

• File:IterEq2plotT.jpg DB F(DB z) { return exp( exp( log(B)*z));} DB G(DB z) { return log( log(z) )/log(B);} (2,922 × 2,922 (1.35 MB)) - 08:38, 1 December 2018

• File:IterPowPlotT.jpg [[Iterate]]s of quadratic function, $T(z)=z^2$: DB F(DB z) { return exp( exp( log(B)*z));} (2,092 × 2,092 (1.06 MB)) - 08:38, 1 December 2018

• File:2014.12.31rudo.png $y=g(z)=f(z)+ (1,452 × 684 (190 KB)) - 08:26, 1 December 2018

• File:Ack3a600.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (5,130 × 1,793 (1.09 MB)) - 08:28, 1 December 2018

• File:Ack3b600.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (5,130 × 1,776 (1 MB)) - 08:28, 1 December 2018

• File:Ack3c600.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (5,130 × 1,776 (1.5 MB)) - 08:28, 1 December 2018

• File:Ack4a600.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (5,130 × 1,776 (1.65 MB)) - 11:57, 21 July 2020

• File:Ack4aFragment.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (3,457 × 1,776 (1.63 MB)) - 08:28, 1 December 2018

• File:Ack4b600.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (5,130 × 1,760 (1.53 MB)) - 11:59, 21 July 2020

• File:Ack4bFragment.jpg int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; z=z_type(x,y); (3,457 × 1,776 (1.62 MB)) - 08:28, 1 December 2018

• File:Ack4c.jpg z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd; z+=z_type(0.1196573712872846, 0.1299776198056910); (5,130 × 1,760 (1.92 MB)) - 08:28, 1 December 2018

• File:Ack4d.jpg z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd; z+=z_type(0.1196573712872846, 0.1299776198056910); (1,282 × 440 (266 KB)) - 08:28, 1 December 2018

• File:Ack4dFragment.jpg 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) );} (3,457 × 1,776 (1.4 MB)) - 08:28, 1 December 2018

• File:Acker2t400.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; (3,555 × 5,588 (1.09 MB)) - 08:28, 1 December 2018

• File:Ackerplot.jpg $A_{\mathrm e,1}(z)=\mathrm e + z$ $A_{\mathrm e,2}(z)=\mathrm e \,z$ (2,800 × 4,477 (726 KB)) - 08:28, 1 December 2018

• File:Ackerplot400.jpg $A_{\mathrm e,1}(z)=\mathrm e + z$ $A_{\mathrm e,2}(z)=\mathrm e \,z$ (3,355 × 4,477 (805 KB)) - 08:29, 1 December 2018

• File:Adpow2map.jpg where $~\mathrm{AdPow}_2(z)=\ln(\ln(1./z))/\ln(a)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,175 × 2,158 (927 KB)) - 08:29, 1 December 2018

• File:Amosaplot.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,092 × 780 (147 KB)) - 08:29, 1 December 2018

• File:Amoscplot.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,092 × 780 (147 KB)) - 08:29, 1 December 2018

• File:Amosmap.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,726 × 1,718 (396 KB)) - 08:29, 1 December 2018

• File:Amosplot.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; ...0){ x=-.82+.005*(n*n); y=Re(Amp(x)); if(n==0)M(x,y) else L(x,y);} //d=Ama(z); (1,394 × 464 (98 KB)) - 08:29, 1 December 2018

• File:Analuxp01t400.jpg This is approximation, function $f$ linear in the ramge $-1 < \Re(z) \le 0$. This approximation had been suggested in 2006 by M.H.Hooshmand $f(z)=\mathrm{uxp}(z)=\!\left\{\!\!\!\! (2,083 × 3,011 (1.67 MB)) - 08:29, 1 December 2018

• File:Analuxp01u400.jpg This is approximation, linear in the ramge $-1 < \Re(z) \le 0$ $\mathrm{uxp}(z)=\!\left\{\!\!\!\! (2,083 × 3,011 (1.72 MB)) - 08:29, 1 December 2018

• File:Analuxp02t900.jpg K_A(z)= ...frac{1}{2}-\frac{1}{2\pi\mathrm i}\ln\frac{1-\mathrm i A+z}{ 1+\mathrm i A-z} \right) (3,362 × 1,295 (987 KB)) - 08:29, 1 December 2018

• File:Anka616map.jpg ...)-1)= \frac{1}{\mathrm e} \, z \exp(z)=\frac{1}{\mathrm e} \, \mathrm{zex}(z)$ where [[zex]] is elementary functions, $\mathrm{zex}(z)=z\,\exp(z)$ (2,641 × 2,625 (1.48 MB)) - 08:29, 1 December 2018

• File:Apow2ma4.jpg [[AuPow]]$_2(z)\!=\!\log_2(\ln(z))~$ and $~$ [[AdPow]]$_2(z)\!=\!\log_2(\ln(1/z))$ (1,779 × 879 (616 KB)) - 08:29, 1 December 2018

• File:Arcnemap11.jpg $\mathrm{Nem}_{p,q}(z)=z+pz^3+qz^4$ int main(){ int Max; int j,k,m,n; DB x,y, p,q,P,Q, t, sr,si,tr,ti; z_type z,c,d,s; (892 × 884 (216 KB)) - 08:30, 1 December 2018

• File:Arcnembrat.jpg $\mathrm{Nem}_q(z)=z+z^3+qz^4$ If $z=\mathrm{NemBra}(q)$, then $\mathrm{Nem}_q'(z)=0$ (2,878 × 2,822 (1.92 MB)) - 08:30, 1 December 2018

• File:Arctra1n3aT.jpg //z_type zex(z_type z){ return z*exp(z);} z_type tra(z_type z){ return z+exp(z);} (2,575 × 2,558 (1.46 MB)) - 08:30, 1 December 2018

• File:Arctra1tesT.jpg \mathrm{ArcTra}_M(1+z)=\sum_{n=1}^M c_n z^n$ \mathcal A(z)= -\lg\left( (2,575 × 2,558 (797 KB)) - 08:30, 1 December 2018

• File:Arctra3tesT.jpg $\mathrm{ArcTra}(z)\approx $ $\mathrm{app3}(z)=$ $ \displaystyle \ln(z) \left(1+ \frac{1}{z} \sum_{m=0}^M \frac{P_m(\ln(z))}{z^m}\right)$ (2,575 × 2,558 (538 KB)) - 08:30, 1 December 2018

• File:Arctra4tesT.jpg $\mathrm{ArcTra}(z)\approx \mathrm{app4}(z)=z-\mathrm e^z$ $ \mathcal A_4(z)= $ $\displaystyle (2,575 × 2,558 (489 KB)) - 08:30, 1 December 2018

• File:ArctranmapT.jpg int main(){ int j,k,m,n; DB x1,x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,575 × 2,558 (1.3 MB)) - 08:30, 1 December 2018

• File:Arknemmap11.jpg $\mathrm{Nem}_{p,q}(z)=z+pz^3+qz^4$ $\mathrm{Nem}(z)=z+pz^3+qz^4$ (892 × 884 (248 KB)) - 08:30, 1 December 2018

• File:Arqnem00zt.jpg 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! (4,192 × 4,192 (749 KB)) - 08:30, 1 December 2018

• File:Arqnem10zt.jpg 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! (4,192 × 4,192 (686 KB)) - 08:30, 1 December 2018

• File:Arqnem20zt.jpg 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! (4,192 × 4,192 (654 KB)) - 08:30, 1 December 2018

• File:Arqnemap11.jpg $\mathrm{Nem}_{p,q}(z)=z+pz^3+qz^4$ z_type nempq(z_type z){ return z*(1.+z*z*(NEMTSOVp+z*NEMTSOVq)); } (1,189 × 1,178 (284 KB)) - 08:30, 1 December 2018

• File:Arqnemplot.jpg 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! (5,230 × 3,154 (495 KB)) - 08:30, 1 December 2018

• File:Aufact.png 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;} (1,677 × 1,324 (171 KB)) - 08:30, 1 December 2018

• File:Aunem00map.jpg 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! (4,441 × 4,317 (1.21 MB)) - 08:30, 1 December 2018

• File:Aunem10map.jpg 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! (4,441 × 4,317 (1.05 MB)) - 08:30, 1 December 2018

• File:Aunem11mbp.jpg z_type T(z_type z){ return z*(1. + z*z*(NEMTSOVp+z*NEMTSOVq)); } // should be suppressed z_type nem(z_type z){ return z + z*z*z*(NEMTSOVp+z*NEMTSOVq); } //new (3,569 × 3,536 (1.16 MB)) - 08:30, 1 December 2018

• File:Aunem1ht.jpg 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! (2,919 × 1,494 (807 KB)) - 08:30, 1 December 2018

• File:Aunem20map.jpg 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! (4,441 × 4,317 (996 KB)) - 08:30, 1 December 2018

• File:Aunem2ht.jpg 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! (2,961 × 1,494 (735 KB)) - 08:30, 1 December 2018

• File:Aunemplot.jpg 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! (8,322 × 8,322 (1.39 MB)) - 08:30, 1 December 2018

• File:Aupow2map.jpg where $~\mathrm{AuPow}_2(z)=\ln(\ln(z))/\ln(a)$ (2,175 × 2,158 (906 KB)) - 08:30, 1 December 2018

• File:AuPow2Plot.jpg DB F(DB z) { return exp( exp( log(B)*z));} DB G(DB z) { return log( log(z) )/log(B);} (1,577 × 1,469 (219 KB)) - 08:30, 1 December 2018

• File:Aupower2map.jpg ...nction]] $G$ of the power transfer function (quadratic function) $T(z)\!=\!z^2$ is shown with $G(z)=\log_2(\ln(z))=\ln^2(z)/\ln(2)$ (2,175 × 2,158 (900 KB)) - 08:30, 1 December 2018

• File:Ausin1susinmapt70.jpg $\sin(z)=\mathrm{SuSin}\big(1+\mathrm{AuSin}(z)\big)$ The range of validity is shown with the [[complex map]] in the $z=z+\mathrm i y$ compex plane; within the range, (2,274 × 2,871 (1.47 MB)) - 08:30, 1 December 2018

• File:Ausinmap52r5.jpg //z_type arcsin(z_type z){ return -I* log(I*z + sqrt(1.-z*z) ); } z_type arcsin(z_type z){ (2,274 × 2,871 (1.24 MB)) - 08:30, 1 December 2018

• File:Ausinplot1.jpg $y=\mathrm{AuSin}(z)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (689 × 904 (61 KB)) - 08:30, 1 December 2018

• File:Ausinsusinmapt50.jpg $~\mathrm{SuSin}\big(\mathrm{AuSin}(z)\big)\!=\!z~$ in the complex plane $~z\!=\!x\!+\!\mathrm i y~$. (2,274 × 2,871 (1,015 KB)) - 08:30, 1 December 2018

• File:Ausintay40t50.jpg 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); (2,274 × 2,871 (1.7 MB)) - 08:30, 1 December 2018

• File:Autran0m10map64t.jpg z_type tra(z_type z) {return z+exp(z);} z_type arctra(z_type z){return z-Tania(z-1.);} (1,254 × 1,670 (440 KB)) - 08:30, 1 December 2018

• File:Autran0m9tes64t.jpg z_type tra(z_type z) {return z+exp(z);} z_type arctra(z_type z){return z-Tania(z-1.);} (1,254 × 1,670 (427 KB)) - 08:30, 1 December 2018

• File:Autran9tes20t1.jpg z_type tra(z_type z) {return z+exp(z);} z_type autran0(z_type z) {z_type e=exp(z); z_type s; int n,M; (4,366 × 4,316 (1.68 MB)) - 08:30, 1 December 2018

• File:Autraplot.jpg z_type tra(z_type z){ return exp(z)+z;} int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("autraplo.eps","w"); ado(o,412,412); (842 × 855 (99 KB)) - 08:30, 1 December 2018

• File:Besselj0map4.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (3,425 × 1,745 (1.47 MB)) - 08:31, 1 December 2018

• File:Boyt.jpg ...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. .. z_type sinn(z_type n, z_type z){return susin(n+ausin(z));} (5,105 × 2,449 (1.17 MB)) - 08:31, 1 December 2018

• File:Boyt100.jpg ...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. .. ...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. .. (3,473 × 1,646 (467 KB)) - 08:31, 1 December 2018

• File:Doya1T.jpg int main(){ int j,k,m,n; DB x,y,t,e, a; z_type z; M(0,0); for(n=1;n<151;n++){x=.02*n;z=x;y=Re(Doya(1.,z)); L(x,y)} (888 × 1,328 (117 KB)) - 08:34, 1 December 2018

• File:E1e14z600.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; k=0;for(m=-40;m<101;m+=1){x=.1*m;z=x;c=exp(exp(z));y=Re(c); if(k==0)M(x,y)else L(x,y);k++; if(y>6)break;} (3,566 × 6,300 (1.85 MB)) - 08:34, 1 December 2018

• File:E1eAuMap600.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (3,543 × 5,338 (1.57 MB)) - 08:34, 1 December 2018

• File:E1eghalfm3.jpg ...xp_{\eta,\mathrm u}^{1/2}(z)=$[[SuExp]]$_{\eta}\big(1/2+$[[SuExp]]$_{\eta}(z)\big)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,750 × 1,341 (1.24 MB)) - 08:34, 1 December 2018

• File:E1egi4.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,236 × 1,660 (828 KB)) - 08:34, 1 December 2018

• File:E1eiterT.jpg id ess, the iterates of the [[transfer function]] $T(z)=\exp(z/\mathrm e)$. $F_3(z\!+\!1)=T( F_3(z))$ (2,166 × 2,179 (1.03 MB)) - 08:34, 1 December 2018

• File:E1eplot8.png $F(z+1)=\exp_b(F(z))$ int main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d; (2,577 × 1,355 (226 KB)) - 08:34, 1 December 2018

• File:E1esuma8.jpg $\exp_\eta(F(z))=F(z+1)$, int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (4,472 × 3,320 (1.76 MB)) - 08:34, 1 December 2018

• File:E1eSuMap600.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (3,377 × 5,055 (1.37 MB)) - 08:34, 1 December 2018

• File:E1etetma8.jpg $\exp_\eta(F(z))=F(z+1)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (4,472 × 3,320 (1.69 MB)) - 08:34, 1 December 2018

• File:E1eti4.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,236 × 1,660 (1.02 MB)) - 08:34, 1 December 2018

• File:Esqrt2ite12mapT80.jpg $T(z)= \exp_{\sqrt{2}}(z)=\big(\sqrt{2}\big)^z$ the $\frac{1}{2}$ iteration is function $f$ such that $f(f(z))=T(z)$ (2,302 × 2,322 (1.41 MB)) - 08:35, 1 December 2018

• File:Esqrt2ite13MapT80.jpg $T(z)= \exp_{\sqrt{2}}(z)=\big(\sqrt{2}\big)^z$ the $\frac{1}{3}$ iteration is function $f$ such that $f(f(f(z)))=T(z)$ (2,302 × 2,322 (1.86 MB)) - 08:35, 1 December 2018

• File:Exp1exp2t.jpg D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. [[Mathematics of Computation]], v.78 (2009), 1647-1670. // z_type tra(z_type z){ return exp(z)+z;} (1,278 × 875 (296 KB)) - 08:35, 1 December 2018

• File:Expitemap.jpg int 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); //if(abs(z+2.)>.019) (1,825 × 2,841 (1.88 MB)) - 08:35, 1 December 2018

• File:Expq2mapT1000.jpg int main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,333 × 2,333 (1.8 MB)) - 08:35, 1 December 2018

• File:Facite.jpg $\mathrm{Factorial}^n(z)=\mathrm{SuFac}\Big(n+\mathrm{AuFac}(z)\Big)$ //DB F(DB z) { return exp( exp( log(B)*z));} (2,092 × 2,092 (799 KB)) - 08:35, 1 December 2018

• File:Facsma.jpg z_type expauno(z_type z) {int n,m; DB x,y; z_type s; s=expaunoc[24]; x=Re(z);if(x<-.9) return expauno(z+1.)-log(z+1.); (975 × 2,366 (164 KB)) - 08:35, 1 December 2018

• File:Figlogzo2t.jpg $z=\mathrm{Filog}(a)~$ expresses solution $z$ of equation $\ln(z)/a=z$. int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,137 × 2,137 (1.84 MB)) - 08:36, 1 December 2018

• File:GoldobinVladimir.jpg https://vk.com/publicya_geroy?z=photo-78250853_341031081%2Falbum-78250853_00%2Frev (720 × 340 (51 KB)) - 08:37, 1 December 2018

• File:GoldobinVladimirFragment.jpg https://vk.com/publicya_geroy?z=photo-78250853_341031081%2Falbum-78250853_00%2Frev (489 × 398 (42 KB)) - 08:37, 1 December 2018

• File:GoldobinVladimirFYigO9UEXwI.jpg https://vk.com/publicya_geroy?z=photo-78250853_341031081%2Falbum-78250853_00%2Frev (450 × 600 (45 KB)) - 08:37, 1 December 2018

• File:Hermigaaplot.jpg [[amos]]$(z)=\,$ $\displaystyle \frac{2^{-n/2}\, \sqrt{z!}} (1,672 × 477 (247 KB)) - 08:37, 1 December 2018

• File:Hermigaplot.jpg int M,m,n; DB x,xx,y,z,s; (1,672 × 435 (160 KB)) - 08:37, 1 December 2018

• File:Hermiten.jpg $\displaystyle h_n(z)= \frac{1}{\sqrt{N_n}} \mathrm{HermiteH}[n,x]=\frac{H_n(x)}{\sqrt{N_n}}$ $\displaystyle N_n=\int_{-\infty}^{\infty} H_n(z)^2 \, \exp(-x^2)\, \mathrm d x=2^n n! \sqrt{\pi}$ (1,257 × 1,473 (227 KB)) - 08:37, 1 December 2018

• File:Hermiten6map.jpg h_n(z)= \frac{ H_n(z)} (1,307 × 880 (630 KB)) - 08:37, 1 December 2018

• File:Itnem00plot.jpg 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! (5,562 × 5,562 (1.36 MB)) - 08:38, 1 December 2018

• File:Itnem10plot.jpg 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! (5,562 × 5,562 (1.32 MB)) - 08:38, 1 December 2018

• File:Itnem20plot.jpg 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! (5,562 × 5,562 (1.3 MB)) - 08:38, 1 December 2018

• File:KelleriteT.jpg z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;} (871 × 880 (493 KB)) - 08:39, 1 December 2018

• File:Koriasmap.jpg For $z\ne1$, funciton [[kori]] appears as $\mathrm{kori}(z)=\displaystyle \frac{J_0\big( L \sqrt{z} \big)}{1-z}$ (1,379 × 1,354 (941 KB)) - 08:40, 1 December 2018

• File:Korifit76map.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (3,262 × 2,400 (1.17 MB)) - 08:40, 1 December 2018

• File:Korifit76plot.jpg \mathrm{mori}(z) \approx \mathrm{korifit76}(z^2)$ (3,831 × 863 (318 KB)) - 08:40, 1 December 2018

• File:Korimap.jpg For $z\ne 1$, [[kori]] can be defined with [[kori]]$(z)=\displaystyle \frac{J_0\big(L_1 \sqrt{z}\big)}{1-z}$ (3,262 × 2,400 (1 MB)) - 08:40, 1 December 2018

• File:KorimapFragment.jpg For $z\ne 1$, [[kori]] can be defined with [[kori]]$(z)=\displaystyle \frac{J_0\big(L_1 \sqrt{z}\big)}{1-z}$ (2,416 × 2,395 (1.49 MB)) - 08:40, 1 December 2018

• File:Koriplot.jpg ...ready provides of order of 15 decimal digits of $\mathrm{kori}(z)$ while $|z|<6$, and still of order of 10 significant figures in the range of the figur int main(){int m,n,i; double x,y,z,t,u; FILE *o; (2,947 × 1,037 (197 KB)) - 08:40, 1 December 2018

• File:Koritestplot.jpg int main(){int m,n,i; double x,y,z,t,u; FILE *o; long double X,Y,Z,T,U; (1,618 × 996 (144 KB)) - 08:40, 1 December 2018

• File:Lofmap.jpg ...er, $\mathrm{lof}(z)$ does not have multiple cut lines (except that along $z\!\le -1$, as $\ln(z!)$ has; in such a way, [[lof]] is holomorphic in the most of the complex p (2,150 × 2,141 (1.96 MB)) - 08:41, 1 December 2018

• File:Lofplot.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,270 × 1,100 (153 KB)) - 08:41, 1 December 2018

• File:Loge1emapT1000.jpg int main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,361 × 2,333 (1.67 MB)) - 08:41, 1 December 2018

• File:Logi2b3t1000.jpg $T(z)=s\, z\,(1\!-\!z)$ for $s\!=\!3$ $T^{0.5}(z)=F(0.5+G(z))$ (1,798 × 1,798 (1.57 MB)) - 08:41, 1 December 2018

• File:Logi2c5T1000.jpg z_type arccos(z_type z){ return -I*log(z+I*sqrt(1.-z*z)); } z_type coe(z_type z){ return .5*(1.-cos(exp((z+1.)/LQ))); } (1,771 × 1,757 (968 KB)) - 08:41, 1 December 2018

• File:Logi2d3t1500.jpg z_type arccos(z_type z){ return -I*log(z+I*sqrt(1.-z*z)); } z_type coe(z_type z){ return .5*(1.-cos(exp((z+1.)/LQ))); } (2,698 × 2,656 (832 KB)) - 08:41, 1 December 2018

• File:Logi2d4t1500.jpg z_type arccos(z_type z){ return -I*log(z+I*sqrt(1.-z*z)); } z_type coe(z_type z){ return .5*(1.-cos(exp((z+1.)/LQ))); } (2,698 × 2,656 (801 KB)) - 08:41, 1 December 2018

• File:Logi2d5t1500.jpg z_type arccos(z_type z){ return -I*log(z+I*sqrt(1.-z*z)); } z_type coe(z_type z){ return .5*(1.-cos(exp((z+1.)/LQ))); } (2,698 × 2,656 (740 KB)) - 08:41, 1 December 2018

• File:Logi2qt.jpg \( T(z)=-1.8\,(-z)^{\sqrt{2}} \) int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,328 × 1,328 (955 KB)) - 17:51, 16 July 2020

• File:Logi2s4t.jpg $T(z)\!=\! s \,z \, (1\!-\!z)$ z_type arccos(z_type z){ return -I*log(z+I*sqrt(1.-z*z)); } (1,328 × 1,328 (906 KB)) - 08:41, 1 December 2018

• File:Logi2s5t.jpg $T(z)=s\, z\,(1\!-\!z)$ for $s\!=\!5$ $T^{0.5}(z)=F(0.5+G(z))$ (2,656 × 2,656 (1.32 MB)) - 08:42, 1 December 2018

• File:Logi5ab400.jpg $T(z)= z\,z\,(1\!-\!z)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,357 × 1,571 (1,000 KB)) - 08:42, 1 December 2018

• File:Logic3T.jpg $T(z)=3\, z\, (1\!-\!z)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,195 × 2,208 (1.16 MB)) - 08:42, 1 December 2018

• File:Logic4T.jpg $T(z)=4 \,z \, (1\!-\!z)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,195 × 2,208 (1.66 MB)) - 08:42, 1 December 2018

• File:Logic5T.jpg [[Iteration]] of the [[Logistic operator]] $T(z)=5\, z\, (1\!-\!z)$, int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,714 × 2,727 (1.92 MB)) - 08:42, 1 December 2018

• File:Logiha300.jpg ...ex map]] of the halfiterate or the [[Logistic operator]] $T(z)\!=\!s \,z\,(z\!-\!1)$ for int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (1,771 × 2,551 (1.81 MB)) - 08:42, 1 December 2018

• File:LogisticSecK2.jpg $F(z\!+\!1) = s F(z)(1-F(z))$ for the logistic operator $\mathrm{LogisticOperator}_s(z)=sz(1-z)$ (6,807 × 3,044 (996 KB)) - 08:42, 1 December 2018

• File:Logq2mapT1000.jpg int main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,361 × 2,333 (1.49 MB)) - 08:42, 1 December 2018

• File:Moriamap1.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,154 × 1,312 (1.44 MB)) - 08:43, 1 December 2018

• File:Moriasmap1.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (2,154 × 1,312 (1.3 MB)) - 08:43, 1 December 2018

• File:Morimap.jpg $\mathrm{mori}(z)= \displaystyle \frac{ J_0(L\, z)}{1-z^2}$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,283 × 1,163 (1.58 MB)) - 08:43, 1 December 2018

• File:Nem00map.jpg $\mathrm{nem}_0(z)=z+z^3$ z_type nem(z_type z) { return z*(1.+z*z*(1.+z*Q)); } (1,784 × 1,768 (540 KB)) - 08:44, 1 December 2018

• File:Nem0map.jpg $\mathrm{Nem}_0(z)=z+z^3$ z_type nem(z_type z) { return z*(1.+z*z*(1.+z*Q)); } (888 × 871 (439 KB)) - 08:44, 1 December 2018

• File:Nem120map.jpg $\mathrm{nem}_2(z)=z+z^3+2z^4$ int main(){ int Max; int j,k,m,n; DB x,y, p,q, t,tr,ti; z_type z,c,d; (1,784 × 1,768 (478 KB)) - 08:44, 1 December 2018

• File:Nem1hht.jpg ...rm{Nem}_1^{1/2}(z)=\mathrm{SuNem}_1\!\left( \frac{1}{2} + \mathrm{AuNem}_1(z) \right)$ z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } (759 × 747 (79 KB)) - 08:44, 1 December 2018

• File:Nem1it.jpg 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! (1,519 × 2,349 (1.14 MB)) - 08:44, 1 December 2018

• File:Nem1map.jpg $\mathrm{nem}_1(z)=z+z^3+z^4$ z_type nem(z_type z) { return z*(1.+z*z*(1.+z*Q)); } (888 × 871 (503 KB)) - 08:44, 1 December 2018

• File:Nem2map.jpg $\mathrm{nem}_2(z)=z+z^3+2z^4$ z_type nem(z_type z) { return z*(1.+z*z*(1.+z*Q)); } (888 × 871 (448 KB)) - 08:44, 1 December 2018

• File:Nembrant.jpg where $z=\mathrm{NemBran}(q)$ is branchpoint of function $z\mapsto\mathrm{ArqNem}_q(z)$ (361 × 871 (65 KB)) - 08:44, 1 December 2018

• File:Nembraplot.jpg for positive $q$. Function [[NemBra]] is solution $z=\mathrm{NemBra}(q)$ $\mathrm{Nem}_q'(z)=0$ (361 × 1,286 (77 KB)) - 08:44, 1 December 2018

• File:Nemplot.jpg [[Explicit plot]] of the [[Nemtsov function]] $\mathrm{Nem}_q(z)=z+z^3+qz^4$: $y=\mathrm{Nem}_q(z)$ versus $x$ for various $q$. (838 × 2,088 (129 KB)) - 08:44, 1 December 2018

• File:Norifit76fragment.jpg int main(){int m,n,i; double x,y,z,t,u; FILE *o; z=Re(korifit76(x)); z*=z; (967 × 448 (155 KB)) - 08:44, 1 December 2018

• File:Norifit76plot.jpg int main(){int m,n,i; double x,y,z,t,u; FILE *o; z=Re(korifit76(x)); z*=z; (1,070 × 448 (168 KB)) - 08:44, 1 December 2018

• File:Norifragment.jpg $\mathrm{nori}(z)=\,$[[mori]]$\big(\sqrt{z}\big)^2$ z_type nori2(z_type z){ int m,n; z_type s; (3,611 × 2,944 (1.71 MB)) - 08:44, 1 December 2018

• File:Norimap40.jpg $\mathrm{nori}(z)=\,$[[mori]]$\big(\sqrt{z}\big)^2$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (2,833 × 2,844 (1.34 MB)) - 08:44, 1 December 2018

• File:Olga6map.jpg $\mathrm{Doya}(\mathrm{Olga}(z))=\mathrm e\, \mathrm{Olga}(z)$ $\mathrm{Olga}(z)=\mathrm{Tania}(\ln(z))$ (2,641 × 2,625 (866 KB)) - 08:45, 1 December 2018

• File:Olgamap.jpg $\mathrm{Doya}(\mathrm{Olga}(z))=\mathrm e\, \mathrm{Olga}(z)$ $\mathrm{Olga}(z)=\mathrm{Tania}(\ln(z))$ (3,475 × 3,458 (551 KB)) - 08:45, 1 December 2018

• File:Penmap.jpg z_type pen0(z_type z){ z_type e=exp(k*z); (2,350 × 2,311 (1.56 MB)) - 08:46, 1 December 2018

• File:Penplot.jpg $\mathrm{pen}(z\!+\!1) = \mathrm{tet}\Big( \mathrm{pen}(z)\Big)$ z_type pen0(z_type z){ (1,266 × 2,100 (240 KB)) - 08:46, 1 December 2018

• File:Penzoo25t400.jpg z_type pen0(z_type z){ z_type e=exp(k*z); (2,833 × 1,177 (1.22 MB)) - 08:46, 1 December 2018

• File:QFacMapT.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y); (1,771 × 1,748 (936 KB)) - 08:48, 1 December 2018

• File:QQFacMT.jpg [[Complex map]] of function $H(z)=h(h(z))$, ...mathrm{Factorial}^{0.5}(z)=\mathrm{SuFac}\left( \frac{1}{2}+\mathrm{AuFac}(z)\right) (885 × 868 (437 KB)) - 08:48, 1 December 2018

• File:SdPow2map.jpg $F(z)=$[[SdPow]]$_2(z)=\exp(-2^z)$ ...ion $F$ is [[superfunction]] for the quadratic transfer function $T(z)\!=\!z^2$, (2,175 × 2,158 (1.47 MB)) - 08:51, 1 December 2018

• File:Shelima600.png z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd; // z+=z_type(0.1196573712872846, 0.1299776198056910); (1,693 × 531 (83 KB)) - 08:51, 1 December 2018

• File:Shelr80.png z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd; //z+=z_type( 0.1196573712872846, 0.1299776198056910); (1,563 × 1,454 (237 KB)) - 08:51, 1 December 2018

• File:Shelre60.png z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd; //z+=z_type( 0.1196573712872846, 0.1299776198056910); (1,172 × 1,090 (142 KB)) - 08:51, 1 December 2018

• File:Sinplo1t100.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; M(0,0) DO(m,158){ x=.01*(m+.1); z=x; c=ausin(z); c=susin(.1*n+c); y=Re(c); (4,469 × 2,352 (1.31 MB)) - 08:51, 1 December 2018

• File:Sinplo2t100.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; M(0,0) DO(m,158){ x=.01*(m+.1); z=x; c=ausin(z); c=susin(.1*n+c); y=Re(c); (4,469 × 2,352 (1.62 MB)) - 08:51, 1 December 2018

• File:Sqrt23uplot.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; for(m=0;m< 84; m+=4) { x=-1.84+.01*m; z=x; y=Re(F21E(z)); if(m==0) M(x,y) else L(x,y)} (1,569 × 4,381 (240 KB)) - 08:52, 1 December 2018

• File:Sqrt27t.jpg int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; for(m=0;m<684;m+=4) { x=-1.84+.01*m; z=x; (3,401 × 3,401 (475 KB)) - 08:52, 1 December 2018

• File:Sqrt27u.png int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; for(m=0;m< 99;m+= 2){x=-1.9999+.01*m; z=x; c=F21E(-F21E(z))+z; y=Re(c);y*=100; if(m==0) M(x,y) else L(x,y)} (856 × 507 (50 KB)) - 08:52, 1 December 2018

• File:Sqrt2atemap.jpg int 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); (1,758 × 1,741 (723 KB)) - 08:52, 1 December 2018

• File:Sqrt2diimap80.jpg int 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); (2,302 × 2,306 (1.27 MB)) - 08:52, 1 December 2018

• File:Sqrt2eitet.jpg DB F(DB z) { return exp( exp( log(B)*z));} DB G(DB z) { return log( log(z) )/log(B);} (3,051 × 3,022 (1.36 MB)) - 08:52, 1 December 2018

• File:Sqrt2q2map600.jpg ...1/2}(z)= \mathrm{tet}_{\sqrt{2}}\left( \frac{1}{2}+\mathrm{ate}_{\sqrt{2}}(z) \right)$ int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; (1,766 × 1,750 (1.43 MB)) - 08:52, 1 December 2018

• File:Sqrt2srav.png z_type exq(z_type z){ DB T4= 19.236149042042854712; DB T2=-17.143148179354847104; z_type z3=z-3.; (2,532 × 1,639 (263 KB)) - 10:53, 24 June 2020

• File:Sqrt2sufuplot.png \( \exp_b(F(z))=F(z\!+\!1) \) int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; (3,520 × 2,507 (408 KB)) - 10:11, 10 June 2022

• File:Sqrt2tetatemap.jpg $\mathrm{tet}_{\sqrt{2}}(\mathrm{ate}_{\sqrt{2}}(z))=z$ in the plane $x=\Re(z)$, $y=\Im(z)$ (1,758 × 1,741 (1,008 KB)) - 08:52, 1 December 2018

• File:Sqrt2tetmap.jpg int 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); (1,758 × 1,741 (656 KB)) - 08:52, 1 December 2018

• File:Sqrt2uiimap80.jpg int 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); (2,302 × 2,306 (1.84 MB)) - 08:52, 1 December 2018

• File:Straro05at.jpg For positive $q$ and complez $z$, function $\mathrm{Straro}_q(z)$ is such that $\mathrm{StraRo}_q(z)^2=27(z\!-\!q)^2+4(1\!+\!4qz)^3$ (2,905 × 2,905 (1.16 MB)) - 08:52, 1 December 2018

• File:Straro10at.jpg For positive $q$ and complez $z$, function $\mathrm{Straro}_q(z)$ is such that $\mathrm{StraRo}_q(z)^2=27(z\!-\!q)^2+4(1\!+\!4qz)^3$ (2,905 × 2,905 (1.49 MB)) - 08:52, 1 December 2018

• File:Straro20at.jpg For positive $q$ and complez $z$, function $\mathrm{Straro}_q(z)$ is such that $\mathrm{StraRo}_q(z)^2=27(z\!-\!q)^2+4(1\!+\!4qz)^3$ (2,905 × 2,905 (1.28 MB)) - 08:52, 1 December 2018

• File:Straroplot.jpg z_type T(z_type z){ return z*(1.+z*z*(1.+z*Q));} z_type F(z_type z){ z_type a,b,r,R ; a=Q-z; b=1. + 4.*Q*z; r = 27.*a*a + 4.*b*b*b ; (1,257 × 1,506 (265 KB)) - 08:52, 1 December 2018

• File:Sunem0ht.jpg $\mathrm{nem}(z)=z+z^3+qz^4$ T[z_] = z + z^3 + q z^4 (2,137 × 1,100 (503 KB)) - 08:53, 1 December 2018

• File:Sunem0map6.jpg $\mathrm{Nem}_q(z)=z+z^3+qz^4$ $F(z\!+\!1)=\mathrm{Nem}_q(F(z))$ (2,615 × 2,594 (1.15 MB)) - 08:53, 1 December 2018

• File:Sunem0mdp.jpg $\mathrm{Nem}_q(z)=z+z^3+qz^4$ $F(z\!+\!1)=\mathrm{Nem}_q(F(z))$ (2,158 × 2,141 (822 KB)) - 08:53, 1 December 2018

• File:Sunem10q10map6.jpg $\mathrm{nem}(z)=z+pz^3+qz^4$ T[z_]=z+p z^3+q z^4 (2,615 × 2,594 (335 KB)) - 08:53, 1 December 2018

• File:Sunem1ht.jpg $\mathrm{nem}(z)=z+z^3+qz^4$ z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } (2,137 × 1,100 (429 KB)) - 08:53, 1 December 2018

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