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

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

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