Search results

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

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 $f={\rm tet}_b(z)$ 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]], 78, 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).  ...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
: $\displaystyle \mathrm {Cip}(z)=\frac{\cos(z)}{z}$  : $\displaystyle \mathrm{Cip}(\mathrm{ArcCip}(z))=z$.

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) 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)$ 

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
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
 This function returns the sum of the complex numbers a and b, z=a+b. ... 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
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
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
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
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
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
Ackermann function
...ven integer number $n$, called "number of Ackermann", function $A_{b,n}(z)$ is called [[Ackermann function]], iff it satisfies the following equatio $A_{b,1}(z)=b+z$

10 KB (1,534 words) - 06:44, 20 July 2020
AdPow
$\mathrm{AdPow}_a(z)=\log_a(\ln(1/z))$ $\mathrm{AdPow}_a(z)=\log_a(\ln(z))$

2 KB (271 words) - 18:43, 30 July 2019
Amos
$\mathrm{Amos}(z)=$ $\displaystyle ...ac{1}{2}\mathrm{Lof}(z)-\mathrm{Lof}\Big(\frac{z}{2}\Big)-\frac{\ln(2)}{2} z \right)$

6 KB (883 words) - 18:44, 30 July 2019
Amplitude of oscillator function
where $\psi_n(z)=\frac{1}{\sqrt{N_n}}$[[HermiteH]]$_n(z)\, \exp(-z^2/2)$ is [[oscillator function]], $\mathrm{lof}(z)= \ln(\mathrm{Factorial}(z)) = \ln(z!)$

6 KB (770 words) - 18:44, 30 July 2019
Analuxpf3c.cin
// In order to evaluate the approximation at artument $z$, type F3(z) z_type F3(z_type z){ DB x=Re(z);

1 KB (253 words) - 18:48, 30 July 2019
ArcTania
$\mathrm{ArcTania}(z)=z+\ln(z)−1$ ...style \mathrm{Tania}^{\prime}(z)=\frac{\mathrm{Tania}(z)}{1+\mathrm{Tania}(z)} \)

1 KB (160 words) - 18:43, 30 July 2019
Arcsin.cin
z_type asin0(z_type z){ int m,M; z_type q,s; DB c[41]={ M=40; q=z*z; s=c[M]*q; for(m=M-1;m>0;m--) {s+=c[m]; s*=q;}

4 KB (488 words) - 06:58, 1 December 2018
Arctran.cin
z_type tra(z_type z){ return z+exp(z);} z_type arctra1(z_type z){ static DB c[22]={0.,0.5,-0.0625,.005208333333333333, // 0 - 3

2 KB (354 words) - 06:58, 1 December 2018
ArqNem
$\mathrm{Nem}(\mathrm{ArqNem}(z))=z$ $\mathrm{Nem}(z)=\mathrm{Nem}_{q}(z)=z+z^3+qz^4$

7 KB (1,319 words) - 18:46, 30 July 2019
Arqnem.cin
// arcnem(z) evaluates $\mathrm{ArcNem}_Q(z)$, while parameter $Q$ should be stored as global variable, together wit z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); }

3 KB (521 words) - 18:48, 30 July 2019
AuNem
[[File:Aunemplot.jpg|300px|thumb|Fig.1: $y\!=\!\mathrm{AuNem}_q(z)$ for ...[[Abel function]] of the [[Nemtsov function]], $\mathrm{Nem}_q(z)=z+z^3+q z^4 ~ ~$, where $q~$ is positive parameter.

9 KB (1,441 words) - 18:45, 30 July 2019
AuPow
$\mathrm{AdPow}_a(z)=\log_a(\ln(z))$ $\mathrm{AdPow}_a(z)=\log_a(\ln(1/z))$

2 KB (284 words) - 18:43, 30 July 2019
AuSin
$\mathrm{AuSin}(\sin(z))=\mathrm{AuSin}(z)+1$ $\mathrm{AuSin}(z)=\mathrm{AuSin}(\pi/2-z)$

5 KB (761 words) - 18:48, 30 July 2019
Ausin.cin
z_type ausin0(z_type z){ z_type b,d,L; int n,N; DB c[32]= N=21; L=log(z); b=z*z; //d=b*(c[N]*.5);

1 KB (156 words) - 06:58, 1 December 2018
Base e1e
\tilde F(z)=\mathrm e\cdot\left(1-\frac{2}{z}\left( 1+\sum_{m=1}^{M} \frac{P_{m}\big(-\ln(\pm z) \big)}{(3z)^m}

4 KB (559 words) - 17:10, 10 August 2020
Base sqrt2
...omplex plane except $z\le 0$, the relation $\exp_b\big( \log_b(z) \big)=z$ takes place. $\log_b\big( \exp_b(z)\big) =z $

3 KB (557 words) - 18:46, 30 July 2019
Conjecture on superfunctions
...in(z))=z holds. Iteration of sin is expressed with sinˆn(z)=SuSin(n+AuSin(z)), where the number n of iteration has no need to be integer. .. D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.

7 KB (1,031 words) - 03:16, 12 May 2021
E1egf.cin
z_type e1egf(z_type z){ int n,N; z_type c,f; // z+= 2.798248154231454;

2 KB (219 words) - 18:48, 30 July 2019
E1egi.cin
z_type E1EGI(z_type z){ z_type p; int n; DO(n,18){ p=z-M_E; if(abs(p)<.3) break; z=log(z)*M_E; }

2 KB (148 words) - 18:47, 30 July 2019
E1etf.cin
z_type e1etf(z_type z){ int n,N; z_type c,f; z+=2.798248154231454;

2 KB (203 words) - 18:48, 30 July 2019
E1eti.cin
z_type E1ETI(z_type z){ z_type p,q,r,u,v; DB a,b,c; int n; ...DO(n,16){ p=M_E-z; if(abs(p)<.6) break; if(Re(z)>1.e8) break; z=exp(z/M_E); }

2 KB (162 words) - 18:47, 30 July 2019
Elementary function
$A_{b,n}(z\!+\!1)=A_{b,n-1}\!\big( A_{b,n}(z)\big)$ ..., the real–holomorphism of ackermanns is assumed, $A_{b,n}(z^*)=A_{b,n}(z)^*$.

3 KB (496 words) - 18:45, 30 July 2019
Exotic iteration
F(z\!+\!1)=T(F(z)) $ \displaystyle \lim_{z\rightarrow \infty} F(z)=L$

11 KB (1,715 words) - 18:44, 30 July 2019
Exp
$\exp'(z)=z$

361 bytes (37 words) - 18:44, 30 July 2019
F15.cin
z_type f15(z_type z){ //NOT SHIFTED FOR x1 !!!! ...K){t=A15*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}

2 KB (272 words) - 07:00, 1 December 2018
Fsexp.nb
...in [[Mathematica]] that evaluates the natural [[tetration]] tet; call SEXP[z] <poem> *) (* c[x_, y_, z_] = RGBColor[x, y, z]; *)

7 KB (306 words) - 07:00, 1 December 2018
Fslog.nb
...tine in Mathematica that evaluates the natural arctetration tet; call SLOG[z] <poem> *) slo[z_] := Sum[Extract[DE, n+1] ((z-1)/2)^n, {n,1,90}] + Log[z-Zo]/Zo + Log[z-Zc]/Zc + Extract[DE,1]

3 KB (126 words) - 07:00, 1 December 2018
Gauss-Legendre quadrature
{ int m,j,i; long double z1,z,xm,xl,pp,p3,p2,p1; { z=cos(M_PI*(i-0.25)/(n+0.5));

3 KB (486 words) - 18:47, 30 July 2019
Gen laguerre rule.cpp
void imtqlx ( int n, double d[], double e[], double z[] ); void imtqlx ( int n, double d[], double e[], double z[] )

35 KB (4,178 words) - 18:48, 30 July 2019
Hermite Gauss mode
[[Hermite Gauss mode]] refers to the specific solution $F=F(x,z)$ of equation then, assuming some large positive $M$, expression $M^2 z/k$ has sense of the coordinate along the propagation of wave, and \(M x/k\

8 KB (1,216 words) - 18:43, 30 July 2019
Hermite polynomial
$\displaystyle h_n(z)= \frac{1}{\sqrt{N_n}} \mathrm{HermiteH}[n,x]=\frac{H_n(x)}{\sqrt{N_n}}$

4 KB (628 words) - 18:47, 30 July 2019
Inverse function
...$f$ is sigh function $g\!=\!f^{-1}$, that in wide range of argument $z$, $f(g(z))\!=\!z$

3 KB (444 words) - 18:43, 30 July 2019
Khuilo
Gazeta Polska, Nr 34 z 20 sierpnia 2014.

4 KB (405 words) - 07:01, 1 December 2018
Kneser expansion
F(z+1)=\exp(F(z)) F(z)=L+\exp(L z)+\sum_{n=2}^{M_0} a_{0,n} \exp(L n z) + O(\exp(L (M_0\!+

2 KB (325 words) - 22:50, 15 August 2020
Kori
For $z\ne 1~$, $~ ~\mathrm{kori}(z)=\displaystyle \frac{J_0\big(L\, \sqrt{x}\big)}{1-z}$

14 KB (1,943 words) - 18:48, 30 July 2019
Korias
For $z\ne1$, function [[kori]] appears as $\mathrm{kori}(z)=\displaystyle \frac{J_0\big( L_1 \sqrt{z} \big)}{1-z}$

2 KB (328 words) - 10:27, 20 July 2020
Korifit76
\mathrm{nori}(z) \approx \mathrm{korifit76}(z)^2\)

4 KB (644 words) - 18:47, 30 July 2019
Korifit76.cin
...function [[korifit76]], that approximates function [[kori]]$(z)$ for $|z|<40$.

914 bytes (87 words) - 18:48, 30 July 2019
LaguerreL
TeXForm[TableForm[Table[Table[LaguerreL[n, m, z], {n, 0, 5}], {m, 0, 8}]]] 1 & 1-z & \frac{1}{2} \left(z^2-4 z+2\right) &

5 KB (759 words) - 18:44, 30 July 2019
Laplacian in spherical coordinates
...s with respect to $n$th coordinate, where $n$ = "$x$", "$y$" or "$z$", and the Schroediner equation for the hydrogen atom. $z= r \sin(\theta)$

8 KB (1,254 words) - 18:44, 30 July 2019
LegendreP
\mathrm{LegendreP}_\ell(z) = \frac{1}{2^\ell \ell !} \frac{\mathrm d\, (z^2\!-\!1)^\ell }

5 KB (611 words) - 18:44, 30 July 2019
Legendre function
\mathrm{LegendreP}_n(z) = \frac{1}{2^n n!} \frac{\mathrm d\, (z^2\!-\!1)^n }

3 KB (442 words) - 18:44, 30 July 2019
Leninopad
http://wiadomosci.onet.pl/tylko-w-onecie/prezes-ipn-sowieckie-pomniki-znikna-z-polskich-miast/p5j7g7 [[Katarzyna Szewczuk]]. Prezes IPN: sowieckie pomniki znikną z polskich miast. //

3 KB (316 words) - 07:02, 1 December 2018
Lethal decision
http://www.tvn24.pl/niepublikowane-nagranie-z-kokpitu-tu-154m,636030,s.html ...Tu-154M do Smoleńska. Jest połączeniem trzech ścieżek dźwiękowych: z mikrofonu i radia dowódcy, drugiego pilota i mikrofonów w kabinie. (http:

15 KB (1,969 words) - 00:25, 26 November 2023
Ln
\ln'(z)=\frac{1}{z}\) $\ln(z)=\exp^{-1}(z)$

296 bytes (44 words) - 18:49, 30 July 2019
Lof
...~\) , that is holomorphic in the most of the complex $z$ plane (except $z\!\le\!-1$). While the real part of the argument $z$ dominates,

3 KB (478 words) - 18:43, 30 July 2019
Maga
$\mathrm {maga}(z)=1-\mathrm{nagc}(z)^2-\mathrm{nags}(z)^2$ ...ation should be chosen in the integrals for [[nagc]]$(z)$ and [[nags]]$(z)$ in order to provide the convergence.

8 KB (1,256 words) - 18:44, 30 July 2019
Mathematics of Computation
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 (344 words) - 07:02, 1 December 2018
Metric space
(M2): ∀x,y,z∈A: d(x,y)+d(y,z)≥d(x,z) such that for any <math>x, y, z \in M</math>, the following holds:

4 KB (636 words) - 18:47, 30 July 2019
Morias.cin
z_type morias(z_type z){ int k,m,n; z_type s,c,t,x; x=1./(z*z); t=-sqrt(2./M_PI/L1/z)/z/z;

2 KB (188 words) - 07:03, 1 December 2018
Morinaga function
where $J_0$ is the zeroth [[Bessel function]], id est, [[BesselJ0]]; $J_0(z)\!=\,$[[BesselJ]]$[0,x]$ \mathrm{morias}_m(z) = - \sqrt{\frac{2}{\pi L_1}} z^{-5/2} \, G_m(z^2)\,

15 KB (2,303 words) - 18:47, 30 July 2019
Naga
[[mori]]$(z)\approx\,$[[morias]]$_m(z)~$, $~z\rightarrow \infty$, with integer $m$ and \mathrm{morias}_m(z) = - \sqrt{\frac{2}{\pi L_1}} z^{-5/2} \, G_m(z^2)\,

5 KB (750 words) - 10:00, 20 July 2020
NemBra
$\mathrm{Nem}_q(z)=z+z^3+qz^4$ $\mathrm{Nem}_q'(z)=1+3z^2+4qz^3$

4 KB (618 words) - 18:46, 30 July 2019
NemBran
...m}_q\) is real–holomorphic, id est, $\mathrm{Nem}_q(z^*)=\mathrm{Nem}_q(z)^*$; this simplifies the consideration. $\mathrm{Nem}_q(z)=z+z^3+q z^4$

3 KB (400 words) - 18:48, 30 July 2019
Nemtsov function
...Then, Nemtsov Function $\mathrm{Nem}$ is defined for complex argument $z$ as follows: (1)$~ ~ ~ ~ ~ ~ \mathrm{Nem}_q(z)= z+z^3+q z^4$

14 KB (2,157 words) - 18:44, 30 July 2019
Nyquist theorem
\mathrm{sinc}(z)=\frac{\sin(z)}{z} $\displaystyle \mathrm{sink}(z)=\mathrm{sink}(\pi z)=\frac{\sin(\pi z)}{\pi z}$

6 KB (944 words) - 18:48, 30 July 2019
Oscillator function
[[qua]]\)(x)=\int_0^x \sqrt{1-z^2}\,\mathrm d z= 

6 KB (846 words) - 18:47, 30 July 2019
Parabolic coordinates
...lation of parabolic coordinates $u,v$ with Cartesian coordinates $\rho, z$ can be expressed with the following relation: $\displaystyle z=\frac{u\!-\!v}{2}$

3 KB (470 words) - 18:43, 30 July 2019
Pentation
$\mathrm{pen}_b(z)=A_{b, 5}(z)$ $\mathrm{pen}(z)=\mathrm{pen}_\mathrm e(z)$.

5 KB (803 words) - 18:48, 30 July 2019
Pluralism
D.Kouznetsov. Solutions of F(z+1)=exp(F(z)) in the complex z plane. Mathematics of Computation, 78 (2009) 1647-1670 William Paulsen and Samuel Cowgill. Solving $F(z+1)=b^{F(z)}$ in the complex plane. Advances in Computational Mathematics, 2017 March

6 KB (950 words) - 18:48, 30 July 2019
Pomeau-Manneville
(1)$~ ~ ~ F(z+1)=T(F(z))= c~ F(z)~ \Big(1-F(z)\Big)$

7 KB (953 words) - 18:47, 30 July 2019
Radial equation for hydrogen atom
$z=\sin(\phi)$ $~\displaystyle \lambda = \frac{Z e^2}{\hbar} \sqrt{\frac{-\mu}{2 E}\,}$

8 KB (1,199 words) - 18:45, 30 July 2019
Scientific fact
$\exp(\mathrm{tet}(z))=\mathrm{tet}(z\!+\!1)$, satisfying certain additional conditions (see [[Superfunctions]] ...-5718-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane. Mathematics of Computation, 78: 1647-1670.

7 KB (995 words) - 01:48, 19 August 2019
SdPow
...e [[superfunction]] of the [[power function]] $~z\mapsto z^a\!=\!\exp(\ln(z) \,a)~$ $\mathrm{SdPow}_a(z)=\exp(a^z)$

1 KB (202 words) - 18:48, 30 July 2019
Series
Kori[z_]=BesselJ[0,BesselJZero[0,1] Sqrt[z]]/(1-z) naga[p_] = Assuming[{Im[p] == 0}, Integrate[Kori[z]^2 Exp[I p z], {z, 0, Infinity}]]

2 KB (325 words) - 18:44, 30 July 2019
Sin
$f''(z)+f(z)=0$ \sin(z)= \frac{\exp(\mathrm i z)-\exp(-\mathrm i z)}{2 ~ \mathrm i }\)

4 KB (680 words) - 18:43, 30 July 2019
Sqrt2f21e.cin
...uate $\mathrm{tet}_{\sqrt{2}}(z)$, the routine should be called as F21E(z) z_type f21E(z_type z){int n; z_type e,s;

1 KB (109 words) - 18:48, 30 July 2019
Sqrt2f21l.cin
//z_type tq2L(z_type z){ int n; z_type e,s,k; z_type f21L(z_type z){ int n; z_type e,s,k;

1 KB (145 words) - 18:47, 30 July 2019
Sqrt2f23e.cin
...uate $\mathrm{tet}_{\sqrt{2}}(z)$, the routine should be called as F23E(z) z_type f23E(z_type z){int n; z_type e,s; DB coefd[24];

2 KB (146 words) - 18:47, 30 July 2019
Sqrt2f23l.cin
...uate $\mathrm{tet}_{\sqrt{2}}(z)$, the routine should be called as F23L(z) z_type f23L(z_type z){ int n; z_type e,s,k;

2 KB (168 words) - 18:47, 30 July 2019
Sqrt2f43e.cin
z_type f43E(z_type z){int n; z_type e,s; DB coeud[23]; e=exp(.32663425997828098238*(z+1.90057764535874));

1 KB (131 words) - 10:44, 24 June 2020
Sqrt2f43l.cin
z_type f43L(z_type z){ int n; z_type e,s; z-=4.;

1 KB (124 words) - 18:46, 30 July 2019
Sqrt2f45E.cin
z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));

1 KB (108 words) - 18:47, 30 July 2019
Sqrt2f45l.cin
z_type f45L(z_type z){ int n; z_type e,s; z-=4.;

1 KB (131 words) - 18:47, 30 July 2019
StraRo
$\mathrm{StraR}_q(z)=\sqrt{27 (q\! -\! z)^2 + 4 (1\!+\! 4 q z)^3} $ 

4 KB (646 words) - 18:47, 30 July 2019
SuNem
$\mathrm{Nem}_{q}(z)=z+z^3+qz^4$ $\mathrm{Nem}_{q}\big( \mathrm{SuNem}_{q}(z)\big)=\mathrm{SuNem}_{q}(z\!+\!1)$.

6 KB (967 words) - 18:44, 30 July 2019
SuPow
...e [[superfunction]] of the [[power function]] $~z\mapsto z^a\!=\!\exp(\ln(z) \,a)~$ $\mathrm{SuPow}_a(z)=\exp(a^z)$

3 KB (405 words) - 18:43, 30 July 2019
SuSin
$(1)~ ~ ~ \mathrm{SuSin}(z\!+\!1)= \sin(\mathrm{SuSin}(z))$ with specific behaviour at infinity, namely, at large $|z|$,

15 KB (2,314 words) - 18:48, 30 July 2019
Sune.cin
// z_type nem(z_type z){ return z*(1.+z*z*(1.+z*Q)); } // z_type nem1(z_type z){ return 1.+z*z*(3.+z*(4.*Q)); } // WARNING: Q is global!

1 KB (228 words) - 07:06, 1 December 2018
Sunem.cin
z_type nem(z_type z){ return z + z*z*z*(NEMTSOVp+z*NEMTSOVq); } //new ...{ int m,n,k; z_type c[22],s; z_type L=log(-z); z_type x=sqrt(-.5/(NEMTSOVp*z));

2 KB (347 words) - 07:06, 1 December 2018
Tet2f4c.cin
z_type f4(z_type z){ //NOT SHIFTED FOR x1 !!!! ...k,K){t=A*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}

2 KB (262 words) - 07:06, 1 December 2018
Vladif5c.cin
z_type f4(z_type z){ //NOT SHIFTED FOR x1 !!!! ...k,K){t=A*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}

3 KB (439 words) - 07:06, 1 December 2018
Vladinaiv49.cin
z_type naiv49(z_type z) // polynonial approximation of tetration z_type s=1.,t=z;

2 KB (101 words) - 14:55, 12 July 2020
Битва между холодильником и телевизором
...билей наклейки с фашистской символикой ("Z") и бегут в соседние страны (где им совсем

21 KB (344 words) - 22:15, 1 October 2022
Бубнов Олег Юрьевич
[[File:BubnovFront-z-400.jpg|200px|thumb|[[Бубнов Олег Юрьевич]] <ref name="mev

28 KB (194 words) - 07:09, 1 December 2018
Вч 08275

88 KB (1,587 words) - 11:26, 13 August 2023

Search results

Page title matches

Page text matches

Navigation menu

Personal tools

Namespaces

Variants

Views

More

Search

.

Tools