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Create the page "Sqrt(2)" on this wiki! See also the search results found.

• 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
• BesselJ0
  : \( \!\!\!\!\!\!\!\!\!\! (2) \displaystyle ~ ~ ~ J_0(0)=1 ~, ~~ J_0'(0)=0\) \frac{ (-z^2/4)^n }
  6 KB (913 words) - 18:25, 30 July 2019
• ArcSinc
  : \( \mathrm{Sinc}(z)= 1-\frac{z^2}{6}+\frac{z^4}{120}-\frac{z^6}{5040}+ : \(\!\!\!\!\!\!\!\! \mathrm{ArcSinc}(1\!-\!t)= \sqrt{6 t} \left(
  4 KB (563 words) - 18:27, 30 July 2019
• Discrete Hankel transform
  f(t) = \sum_{m=1}^\infty (2 J_\nu(j_{\nu,m}t) / J_{\nu+1}(j_{\nu,m})^2) g_m. g_m = (2 / j_{\nu,M}^2)
  7 KB (1,063 words) - 18:25, 30 July 2019
• Guiding of waves between absorbing walls
  ...aystyle \!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \hat H = \frac{-\hbar^2}{2m} \nabla^2\) The substitution of (2),(3),(4) into (1) gives the "monochromatic" equation
  5 KB (743 words) - 18:47, 30 July 2019
• BesselK0
  : \( \!\!\!\!\!\!\!\!\!\!\ (2) ~ ~ ~ \displaystyle K_0(z) = \exp(-z)\sqrt{\frac{\pi}{2z}} ~ \Big( 1+ O(1/z)\Big)
  3 KB (394 words) - 18:26, 30 July 2019
• BesselY0
  \displaystyle Y_0(x)=\frac{-2}{\pi} \int_0^\infty \cos(x \cosh(t)) \mathrm d t\) : \(Y_0(z)=Y_0(-z)+2~ \mathrm i~ J_0(-z)\)
  3 KB (445 words) - 18:26, 30 July 2019
• BesselJ1
  f''(z)+f'(z)/z + (z^2\!-\!1)f(z) = 0\) : \(f(0) = 0~\) and \(~f'(0)=1/2\)
  3 KB (439 words) - 18:26, 30 July 2019
• Besselj0.cin
  - 9./4.)*u + 2.)* c; return (C+S)/sqrt(2.*M_PI*z);}
  2 KB (190 words) - 18:47, 30 July 2019
• Besselj1.cin
  return s*z/2.;} f=M_PI/4.+z; c=cos(f); s=sin(f); a=sqrt(2./M_PI/z); t=1./(z*z);
  2 KB (159 words) - 14:59, 20 June 2013
• Bessel function
  \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) f(x) \approx x^\nu \left( \frac{2^{-\nu}}{\mathrm{Factorial}(\nu)}+ O(x^2) \right)\)
  13 KB (1,592 words) - 18:25, 30 July 2019

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