File:Rational Elliptic Function (abs, n=4, x=(0,5)).svg

Description
English: A graph of thr absolute value of the fourth-order rational elliptic function, R4(ξ,x) over the interval [0,5]. Here, ξ (the selectivity factor) is 1.4. Also shown is the discrimination factor, Ln.
Date
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Author Inductiveload
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Category:Self-published work#Rational%20Elliptic%20Function%20(abs,%20n=4,%20x=(0,5)).svgCategory:PD-self#Rational%20Elliptic%20Function%20(abs,%20n=4,%20x=(0,5)).svg

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];

(*Use the particular forms for these low-order REFs*)
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
   ];
   
LogPlot[
 xi = 1.4;
 Abs[r4[xi, x]],
 {x, 0, 5},
 PlotRange -> {0.01, 100000}]
Category:Rational functions Category:SVG x-y functions Category:Elliptic functions Category:Images with Mathematica source code
Category:Elliptic functions Category:Images with Mathematica source code Category:PD-self Category:Rational functions Category:SVG x-y functions Category:Self-published work