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Factorial
| 2 || 2 :<math> n! = n \cdot (n-1) \cdots 2 \cdot 1 , \,</math>

27 KB (3,925 words) - 18:26, 30 July 2019
Tetration
...\(b\!>\!1\), is holomorphic at least in \(\{ z \in \mathbb C : \Re(z)\!>\!-2\}\). http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html 

21 KB (3,175 words) - 23:37, 2 May 2021
Tetre2215.cc
// for \(-2<x<2\) and \(1<b<5\) the \(x\),\(b\) coordinates shown with lines \(f=\)const.<b z_type old0(z_type d){ z_type q=sqrt(d); return -1.0018

6 KB (1,030 words) - 18:48, 30 July 2019
4t1c.cc
{ -7.5, 81.4, 6.2, 2}, { -39.0, 80.0, 6.2, 3},

3 KB (564 words) - 18:33, 28 April 2023
Mapping
http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.

14 KB (2,275 words) - 18:25, 30 July 2019
Superfunction
[[Image:Sqrt(factorial)LOGOintegralLOGO.jpg|200px]] [[File:QexpMapT400.jpg|200px]] <center> \(u+\mathrm i v=\sqrt{\exp} (x+\mathrm i y)\)</center>

25 KB (3,622 words) - 08:35, 3 May 2021
Место науки в человеческом знании
2. Постепенное изменение генотипа из 48 хр ...ец. Заседание Президиума. 'Наука Урала' No. 2 (830), январь 2003.

111 KB (2,581 words) - 16:54, 17 June 2020
Logiu.cin
C3=2. /((1.-Q)*(1.-Q2) C5=2.*(7.+Q*(3.+Q*2.)) /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4

3 KB (513 words) - 18:48, 30 July 2019
Square root of factorial
...le:SquareRootOfFactorial.png|400px|right|thumb| \(y\!=\! x!\) and \(y\!=\!\sqrt{!\,}(x)\) verus \(x\)]] [[Square root of factorial]] (half-iteration of [[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\).

13 KB (1,766 words) - 18:43, 30 July 2019
Arcfactorial
: \(\mathrm{ArcFactorial}(2)=2\) ...aystyle \mathrm{ArcFactorial}\left( \frac{\sqrt{\pi}}{2}\right)\!=\frac{1}{2}\)

3 KB (414 words) - 18:26, 30 July 2019
Holomorphic extension of the Collatz subsequence
n/2 , \mathrm{ ~~if~~ } n/2 \in \mathbb N \\ (3n\!+\!1)/2 ~ \mathrm{~~over-vice}

5 KB (798 words) - 18:25, 30 July 2019
Regular Iteration
http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.

20 KB (3,010 words) - 18:11, 11 June 2022
SuperFactorial
..." is [[superfunction]] of [[factorial]] constructed at its [[fixed point]] 2. The smallest integer larger than 2 (id est 3) is chosen as its value at zero, \(\mathrm{SuperFactorial}(0)=3~\

18 KB (2,278 words) - 00:03, 29 February 2024
Abel function
: \(T^2(z)=T(T(z))\) ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-175

4 KB (547 words) - 23:16, 24 August 2020
Transfer function
http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html ...H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.

11 KB (1,644 words) - 06:33, 20 July 2020
Nest
:\(\sqrt{!\,}(z)=\mathrm{Nest}[\mathrm{Factorial},z,1/2]\) ...n function Nest is usable; for example, expression \(~\mathrm{Nest}[\sin,z,2]~\) returns \(~\sin(\sin(z))~\).

3 KB (438 words) - 18:25, 30 July 2019
Japan
...an allows the nation to avoid big conflicts at least since the [[World War 2]]. Such a culture seems to be somehow related with the language, although t ...of the [[Physics Department of the Moscow State University]]), id est, \(\sqrt{!\,}\), !-->

15 KB (2,106 words) - 13:37, 5 December 2020
Quantum reflection
::\( \displaystyle \lambda\left(x\right)=\frac{h}{\sqrt{2m\big(E-V(x)\big)}} \) ...suddenly switched-off. Then, the speed of atoms is determined as <math>~v=\sqrt{2gh}~</math>, where <math>~g~</math> is [[acceleration of free fall]], and

16 KB (2,453 words) - 18:26, 30 July 2019
Ridged mirror
...'' of period <math>~L~</math>; this estimate is valid at <math>KL\!~\theta^2\ll 1</math>. See [[quantum reflection]] for the approximation (fit) of the <math>~\displaystyle r \approx \exp\!\left(-\sqrt{8\!~K\!~L}~\theta\right)~</math>, <!--where <math> ~K~</math> is wavenumber

6 KB (906 words) - 07:04, 1 December 2018
ArcTetration
For base \( b\!=\!\mathrm e \!\approx\! 2.71 \), the natural ArcTetration is presented in figure at right with the [[ ...special function. [[Vladikavkaz Mathematical Journal]], 2010, v.12, issue 2, p.31-45.

7 KB (1,091 words) - 23:03, 30 November 2019
B271az.cc
// for(m=-2;m<0;m+=2) {M(-4.6,m-.2) fprintf(o,"(%1d)s\n",m);} // for(m= 0;m<3;m+=2) {M(-4.4,m-.2) fprintf(o,"(%1d)s\n",m);}

3 KB (529 words) - 14:32, 20 June 2013
Mathematica
...plify]] does not seem to handle well expressions with imaginary unity , I=\Sqrt[-1] . b = (-1 + Exp[(-2*I)*q - 2*s])*(-1 + Exp[(2*I)*q - 2*s])

12 KB (1,901 words) - 18:43, 30 July 2019
Время
...ссия, расследовавшая катастрофу [[Катынь-2]] (10 апреля 2010 года), перевела часы на 15 мин ...ноября 2009 года уведомлений о проведении 2 декабря того же года траурных митингов, п

22 KB (406 words) - 00:38, 30 October 2020
Yulya function
\frac{a\!+\!x}{\sqrt{1-(a\!+\!x)^2}}-\frac{a\!-\!x}{\sqrt{1-(a\!-\!x)^2}} :\( \!\!\!\!\! \!\!\!\!\! \!\!\!\!\! \!\!(2) ~ ~ ~ ~ \mathrm{Yulya}_a\!\Big( \mathrm{ArcYulya}_a(z) \Big) = z\)

12 KB (1,754 words) - 18:25, 30 July 2019
Tania function
: \(\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \displaystyle (2) ~ ~ ~ Tania function has two [[branch point]]s: \(~ -\!2\!\pm\! \mathrm i \pi~\). The position of the [[cut line]]s depends on the r

27 KB (4,071 words) - 18:29, 16 July 2020
Doya function
: \( \displaystyle \!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \mathrm{Doya}(z)= \mathrm{Tania}\!\Big(1+\mathrm{ArcTania}(z)\Big)\) :\(t\!=\!2\), id est, \(~\mathrm{Doya}^2(x)=\mathrm{Doya}\big(\mathrm{Doya}(x)\big)\)

19 KB (2,778 words) - 10:05, 1 May 2021
Doya.cin
)))))); DO(n,2) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; } // +x*(.2 +m*(-25./12 +m*(35./6. +m*(-5. +m)))) //reserve term for the testing

3 KB (480 words) - 14:33, 20 June 2013
Fourier transform
: \(\!\!\!\!\!\!\!\!\!\!\!\!\!(1) ~ ~ ~ \displaystyle B(x)= \frac{1}{\sqrt{2\pi}} \int_{- \infty}^{\infty} \exp( - \mathrm{i} x y) A(y) ~ \mathrm{d} y \ ...!\!\!\!\!\!\!\!\!\!(2) ~ ~ ~ \displaystyle (\hat ふ A)(x)= \frac{1}{\sqrt{2\pi}} \int_{- \infty}^{\infty} \exp( - \mathrm{i} x y) A(y) ~ \mathrm{d} y

11 KB (1,501 words) - 18:44, 30 July 2019
Fafo.cin
// n should be 2^m ; o should be 1 or -1 ; q=N/2; p=2; for(m=1;p<N;m++) p*=2;

1 KB (238 words) - 14:33, 20 June 2013
FFT
B_k=\sum_{m=0}^{N-1} A_m \exp\Big(-\mathrm{i} \frac{2 \pi}{N}~ k~ m\Big)\) where \(N\) is natural number; usually, \(2^n\) for some natural \(n\); 

6 KB (1,010 words) - 13:23, 24 December 2020
Table of superfunctions
: \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \) | \(\displaystyle \frac{-a^2}{z}\)

11 KB (1,565 words) - 18:26, 30 July 2019
Square root of exponential
[[Square root of exponential]] \(\varphi=\sqrt{\exp}=\exp^{1/2}\) is half-iteration of the [[exponential]], id est, such function that its Function \(\sqrt{\exp}\) should not be confused with

5 KB (750 words) - 18:25, 30 July 2019
Iteration
...T.jpg|400px|thumb|Fig.1. Iterates of \(T(z)=z^2~\): \(~y\!=\!T^n(x)\!=\!x^{2^n}~\) for various \(n\)]] [[File:FacIteT.jpg|400px|thumb|Fig.2. Iterates of [[Factorial]]: \(~y\!=\!\mathrm{Factorial~}^{~n}(x)~\) for va

14 KB (2,203 words) - 06:36, 20 July 2020
Fourier-2 transform
'''Fourier-2 transform''' is bidimensional [[Fourier transform]] \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! g(x,y)= \frac{1}{2\pi} \) \(\displaystyle\iint \mathrm dp ~\mathrm dq~ \exp(-i p x - i q y ) ~

6 KB (954 words) - 18:27, 30 July 2019
Квадратный корень из факториала
[[File:SquareRootOfFactorial.png|400px|right|thumb| \(y\!=\! x!\) и \(y\!=\!\sqrt{!\,}(x)\) как функции от \(x\)]] ...из факториала ([[Square root of factorial]]), то есть \(\sqrt{\,!\,}\) - голоморфная функкция \(f\) такая, что

6 KB (312 words) - 18:33, 30 July 2019
Iterated integral
(id est, \(\sqrt{-\!1}~\) ) in [[Mathematica]] and the [[Identity function]], which is also : \(\!\!\!\!\!\!\!\!\! (2)\displaystyle ~ ~ ~ J^m J^n = J^{m+n}\)

9 KB (1,321 words) - 18:26, 30 July 2019
Корень из факториала
Символ \(\sqrt{\,!\,}\) установлен в качестве эмблемы Физфа

7 KB (381 words) - 18:38, 30 July 2019
Filog.cin
z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t); if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);

2 KB (258 words) - 10:19, 20 July 2020
Filog
...anchpoint \(z=1/\mathrm e\); the second goes through the point \(z\!=\!\pi/2\), where the fixed points of logarithm are \(\pm \mathrm i\). ...f the cut, the function has real values; in addition, at \(z=\ln\big(\sqrt{2}\big)\), these values are integer

4 KB (572 words) - 20:10, 11 August 2020
ArcCos
:\( \displaystyle \arccos(z)=\frac{\pi}{2} - \arcsin(z)\) : \(\displaystyle \arccos[z]=\frac{\pi}{2}- \mathrm i ~ \mathrm{arccosh}(\mathrm i \, z)\)

5 KB (754 words) - 18:47, 30 July 2019
ArcCip
: \(\displaystyle \mathrm{Cip}(z) = \frac{1}{z} -\frac{z}{2}+\frac{z^3}{24}+\frac{z^5}{720}+...~\), \(~ |z|\!\ll\! 1\) ...\mathrm{Cip}'(z)=0\) has several solutions. One of them is \(z=f_0\approx 2.798386045783887\) .

8 KB (1,211 words) - 18:25, 30 July 2019
Fac.cin
1.01152306812684171, 1.51747364915328740, 2.26948897420495996, 3.00991738325939817, return s + log(2.*M_PI)/2. - z + (z+.5)*log(z);

4 KB (487 words) - 07:00, 1 December 2018
ArcSin
: \(\displaystyle \sin(z) = \frac{\exp(\mathrm i z)- \exp(-\mathrm i z)}{2~ \mathrm i}\) \( \arcsin(z)= -\mathrm i \ln\Big( \mathrm i z + \sqrt{1-z^2} \big)\)

9 KB (982 words) - 18:48, 30 July 2019
ArcCosc
: \(\mathrm{Sazae} \approx ~ 2.798386045783887\) \frac{2(z\!-\!\mathrm{Tarao})}

8 KB (1,137 words) - 18:27, 30 July 2019
Acosc.cin
z_type acoscL(z_type z){ int n; z_type s,q; z*=-I; q=I*sqrt(1.50887956153832-z); z_type acoscB(z_type z){ z_type t=0.33650841691839534+z, u=sqrt(t), s; int n;

1 KB (219 words) - 18:46, 30 July 2019
Acosc1.cin
if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );} else{return I*log( z - sqrt(z*z-1.) );}}

3 KB (436 words) - 18:47, 30 July 2019
Acosc1
..._1 - \sqrt{ \frac{2}{\mathrm{Tarao}_1 } (\mathrm{Tarao}_1\!-\!x) } + \frac{2\, (\mathrm{Tarao}_1 \!-\! x )}{3~ \mathrm{Sazae}_1~ \mathrm{Tarao}_1}\) \sqrt{

6 KB (896 words) - 18:26, 30 July 2019
ArcFactorial
: \(\mathrm{ArcFactorial}(2)=2\) ...aystyle \mathrm{ArcFactorial}\left( \frac{\sqrt{\pi}}{2}\right)\!=\frac{1}{2}\)

3 KB (376 words) - 18:26, 30 July 2019
Bessel transform
\(\mathrm{HankelKernel}(p,x)= \frac{1}{2 pi} \mathrm{BesselJ}_\nu(2 \pi px)\) \(\mathrm{BesselKernel}(p,x)= \mathrm{BesselJ}_\nu(2 \pi px)\)

8 KB (1,183 words) - 10:21, 20 July 2020
Absorbing Schroedinger
...\!\!\!\! (2) ~ ~ ~ \mathrm i ~ \hbar ~ \dot \Psi = \frac{-\hbar^2 \nabla^2}{2m} \Psi + U(\vec x) ~ \Psi -\mathrm i ~ V(\vec x) ~ \Psi \) : \(\displaystyle \!\!\!\!\!\!\!\!\!\! (7) ~ ~ ~ \omega - (c+\mathrm i s)^2 = -\mathrm i \gamma\)

15 KB (2,070 words) - 18:47, 30 July 2019

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