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File:Rational Elliptic Functions (xi varied, x=(-1,1)).svg

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Description
English: A graph of the fourth-degree rational elliptic function, R4(ξ,x) on the interval [−1,1]. ξ is the selectivity factor, and is varied in this graph.
Date
Source Own work
Author Inductiveload
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Mathematica Code

xp2[xi_] :=
  Module[{g, num, den},
   g = Sqrt[4*xi^2 + (4*xi^2*(xi^2 - 1))^(2/3)];
   num = 2*xi^2*Sqrt[g];
   den = Sqrt[8*xi^2*(xi^2 + 1) + 12*g*xi^2 - g^3] - Sqrt[g^3];
   num/den
   ];
xz2[xi_] := xi^2/xp2[xi];

t[xi_] := Sqrt[1 - 1/xi^2];

r1[xi_, x_] := x;
r2[xi_, x_] := ((t[xi] + 1)*x^2 - 1)/((t[xi] - 1)*x^2 + 1);
r3[xi_, x_] := 
  x*((1 - xp2[xi])*(x^2 - xz2[xi]))/((1 - xz2[xi])*(x^2 - 
        xp2[xi]));
r4[xi_, x_] :=
  Module[{num, den},
   num = (1 + t[xi]) (1 + Sqrt[t[xi]])^2*x^4 - 
     2 (1 + t[xi]) (1 + Sqrt[t[xi]])*x^2 + 1;
   den = (1 + t[xi]) (1 - Sqrt[t[xi]])^2*x^4 - 
     2 (1 + t[xi]) (1 - Sqrt[t[xi]])*x^2 + 1;
   num/den
   ];
   
Plot[
 Table[
  r4[xi, x],
  {xi, {1.0001, 1.001, 1.01, 1.1, Infinity}}],
 {x, -1, 1},
 Axes -> False]

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29 January 2009

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Date/TimeThumbnailDimensionsUserComment
current04:02, 29 January 2009Thumbnail for version as of 04:02, 29 January 2009720 × 460 (96 KB)Inductiveloadfixed y-axis title
03:56, 29 January 2009Thumbnail for version as of 03:56, 29 January 2009720 × 460 (96 KB)Inductiveload{{Information |Description={{en|1=a}} |Source=Own work by uploader |Author=Inductiveload |Date=2009/01/29 |Permission={{PD-self}} |other_versions= }} <!--{{ImageUpload|full}}--> Category:Special functions Category:XY plots

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