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• Bessely0.cin
  +q*(-0.016073968025938425623 + 0.0099471839432434584856 *L //2 +q*(-7.693079900902931853e-10 + 2.9981625986338549158e-10*L //6
  4 KB (370 words) - 18:46, 30 July 2019
• BesselH0
  TeXForm[Expand[Series[(HankelH1[0, x]) (Pi I x/2)^(1/2), {x, Infinity, 5}]]] \(e^{i x} \left(1-\frac{i}{8 x}-\frac{9}{128 x^2}+\frac{75
  4 KB (509 words) - 18:26, 30 July 2019
• CosFourier
  ...\!\!\!\!\!\!\!\! (1) \displaystyle ~ ~ ~ ふ_{\mathrm C}(x,y)=\sqrt{\frac{2}{\pi}} \cos(xy)\) : \(\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \displaystyle \mathrm{CosFourier} f (x) = \int_0^\infty ~ ふ_{\mat
  6 KB (915 words) - 18:26, 30 July 2019
• Discrete Fourier
  ...displaystyle ふ_{m,n}=\frac{1}{\sqrt{N}} \exp\! \left( \frac{- \mathrm i ~2 ~\pi}{N}~m~n\right)\) Sometimes, the operator that deviate from \(\hat ふ\) with factor \(\sqrt{N}\) is considered; for such modified operator, the equation (4) does not h
  6 KB (1,032 words) - 18:48, 30 July 2019
• DiscreteCos
  ...!\!\!\!\!(1) ~ ~ ~ \displaystyle \mathrm{CosFourier}(F)(x) ~=~ \sqrt{\frac{2}{\pi}}~ \int_0^\infty \! \cos(xy) ~F(y)~ \mathrm d y\) ...isplaystyle G_k = (\mathrm{DCTI}_N F)_k = \frac{1}{2} F_0 + \frac{(-1)^k}{2} F_{N} + \sum_{n=1}^{N-1} F_n \cos\! \left(\frac{\pi}{N} n k \right)~\) fo
  3 KB (482 words) - 18:26, 30 July 2019
• Cosft.cin
  for(i=1;i<n;i+=2){ while (m >= 2 && j > m) { j -= m; m >>= 1; }
  4 KB (571 words) - 15:00, 20 June 2013
• DCTIV
  <math>\displaystyle (\mathrm{DCTIV} ~f )_k = \sqrt{\frac{2}{N}} ~ ...~f_n~ \cos \left[\frac{\pi}{N} \left(n+\frac{1}{2}\right) \left(k+\frac{1}{2}\right) \right] \quad \quad k = 0, \dots, N-1.</math>
  3 KB (421 words) - 18:26, 30 July 2019
• DCTI
  ...isplaystyle G_k = (\mathrm{DCTI}_N F)_k = \frac{1}{2} F_0 + \frac{(-1)^k}{2} F_{N} + \sum_{n=1}^{N-1} F_n \cos\! \left(\frac{\pi}{N} n k \right)~\) fo : \( \!\!\!\!\!\!\!\!\!\!(2) ~ ~ ~ ~ (ふ_{\mathrm C1,N}~ F)_k=
  10 KB (1,447 words) - 18:27, 30 July 2019
• Varipend3
  ..., the two cords that connect it with elementary body 1 and elementary body 2 are removed (cut); so, the 0th body remain free. However elementary body 2 and elementary body 3 are still connected with the ideal cord of length uni
  8 KB (1,036 words) - 18:25, 30 July 2019
• DCT
  :<math>X_k = \frac{1}{2} (x_0 + (-1)^k x_{N}) For \(N=2^q\), the evaluation requires of order of \(Nq\) operations.
  10 KB (1,689 words) - 18:26, 30 July 2019
• 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

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