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• DCTII
  _k = \sum_{n=0}^{N-1} ~ F_n~ \cos \left(\frac{\pi}{N} \left(n\!+\!\frac{1}{2}\right) k \right) ~ ~ ~\), \(~ ~ ~ k = 0, \dots, N\!-\!1\) For the simple and efficient implementation, \(N=2^q\) for some natural number \(q\). Note that the size of the arrays is for
  5 KB (682 words) - 18:27, 30 July 2019
• Efjh.cin
  C3=2. /((1.-Q)*(1.-Q2) C5=2.*(7.+Q*(3.+Q*2.)) /((1.-Q)*(1.-Q2)*(1.-Q3)*(1.-Q4
  3 KB (364 words) - 07:00, 1 December 2018
• Logistic operator
  ...ion of the logistic sequence. Moscow University Physics Bulletin, 2010, No.2, p.91-98. (Russian version: p.24-31) : \(\!\!\!\!\!\!\!\!\!\!\!(2) ~ ~ ~ ~ F(z\!+\!1)=T(F(z))\)
  6 KB (817 words) - 19:54, 5 August 2020
• Shoko function
  The [[Shoko function]] is periodic; the period \(P=2 \pi \mathrm i\) is pure imaginary. The [[Shoko function]] has series of branchpoints at \(r+\pi(1\!+\!2 n) \mathrm i\) for integer values of \(n\);
  10 KB (1,507 words) - 18:25, 30 July 2019
• F45E.cin
  ...tion of the [[superfunction]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed point \(L\!=\!4\). 0.12022125769065893274e-1, 0.45849888965617461424e-2,
  1 KB (139 words) - 18:48, 30 July 2019
• F45L.cin
  ...tion of the [[Abel function]] of the [[exponential]] to base \(b\!=\!\sqrt{2}\), constructed at the fixed point \(L\!=\!4\). -0.587369764200886206e-2, 0.289686728710575713e-2,
  2 KB (163 words) - 18:47, 30 July 2019
• Tania.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);
  1 KB (209 words) - 15:01, 20 June 2013
• LambertW.cin
  , 2.66666666666667 z_type LambertWe(z_type z){ int n,m=100; z_type t=1./M_E+z; t*=2*M_E; t=sqrt(t);
  5 KB (287 words) - 15:01, 20 June 2013
• Schroeder equation
  (2) \(~ ~ ~ \log_s\Big(~ g\big( T(z)\big)~\Big) = 1 + \log_s\big(g(z)\big)~\) The substitution of (3) into (2) gives for function \(~G~\) the [[Abel equation]]
  8 KB (1,239 words) - 11:32, 20 July 2020
• Zooming equation
  (2) \(~ ~ ~ g\big(T(z)\big)= K \, g(z) \) http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html
  10 KB (1,627 words) - 18:26, 30 July 2019
• ArcTra
  ...|thumb| \(u\!+\!\mathrm i v\!=\! \mathrm{ArcTra}(x\!+\!\mathrm i y)~\) by (2)]] (2) \(~ ~ ~ \mathrm{ArcTra}(z)=z-\mathrm{Tania}(z-1)\)
  10 KB (1,442 words) - 18:47, 30 July 2019
• AuTra.cin
  z_type sutra(z_type z){ if( Re(z)<2. ) return sutra0(z); if( Re(z)<4. ) return tra(tra(sutra0(z-2.)));
  1 KB (197 words) - 15:03, 20 June 2013
• Simplify
  Simplify[2 Sin[x] Cos[x]] Sin[2 x]
  2 KB (259 words) - 18:45, 30 July 2019
• MathJax
  \( abcd^2 \) <math>f_1(x)=\frac{x+1}{\sqrt{1-x^2}}\label{ref1}\</math>
  5 KB (795 words) - 10:28, 26 March 2021
• Maps of tetration
  [[File:Ack3a600.jpg|400px|thumb|Base \(b=\sqrt{2}\approx 1.41\)]] [[File:Ack4a600.jpg|400px|thumb|Binary tetration, \(b=2\)]]
  5 KB (761 words) - 12:00, 21 July 2020
• Aunemco.txt
  // Q has sense of parameter of the [[Nemtsov function]]; K=Q^2 C[2]=-0.625 + (-0.25 + K/2.)*K;
  16 KB (1,450 words) - 06:58, 1 December 2018
• Nori
  ...|thumb|\(u\!+\!\mathrm i v=\mathrm{mori}\big(\sqrt{x\!+\!\mathrm i y}\big)^2=\mathrm{nori}(x\!+\!\mathrm i y)\)]] ...thumb| \(u\!+\!\mathrm i v=\mathrm{mori}\big(\sqrt{x\!+\!\mathrm i y}\big)^2\)]]!-->
  13 KB (1,759 words) - 18:45, 30 July 2019
• Mathematical notations
  Some of numbers have own single-character names: 0,1,2,3,4,5,6,7,8,9. For example, : <math> 2=1++</math>
  5 KB (753 words) - 18:47, 30 July 2019
• Mandelbrot polynomial
  \( P_c(z)=z^2+c\) \(p(z) = r z -r/2\),
  2 KB (229 words) - 18:44, 30 July 2019
• Iterate of linear fraction
  [[File:Fracit20t150.jpg|300px]]\( t(z)=\frac{z}{2+z} ~\); \(~y=t^n(x)\) versus \(x\) for various \(n\) (07) \(~ ~ ~ \displaystyle T(z)=P(t(Q(z)))= \frac{ABc - AB - A^2 ~+~ (A\!+\!B)z}{Bc-A+z}\)
  13 KB (2,088 words) - 06:43, 20 July 2020

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