File:Rational Elliptic Function (abs, n=3, x=(0,5)).svg
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DescriptionRational Elliptic Function (abs, n=3, x=(0,5)).svg |
English: A graph of thr absolute value of the third-order rational elliptic function, R3(ξ,x) over the interval [0,5]. Here, ξ (the selectivity factor) is 1.4. Also shown is the discrimination factor, Ln. |
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Date | ||||
Source | Own work | |||
Author | Inductiveload | |||
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Mathematica Code edit
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[r3[xi, x]], {x, 0, 5}, PlotRange -> {0.01, 1000}]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 05:00, 29 January 2009 | 720 × 460 (84 KB) | Inductiveload (talk | contribs) | changed to exponent y-labels | |
04:32, 29 January 2009 | 720 × 460 (77 KB) | Inductiveload (talk | contribs) | {{Information |Description={{en|1=A graph of thr absolute value of the third-order en:rational elliptic function, ''R''<sub>3</sub>(''ξ,x'') over the interval [0,5]. Here, ξ (the selectivity factor) is 1.4. Also shown is the discrimination fac |
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