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 particular values for low-order functions*) 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]));  (*Use nesting property for higher-degree functions*) r4[xi_, x_] := r2[r2[xi, xi], r2[xi, x]];  ellgain[xi_, w_, w0_, ep_] := 1/Sqrt[1 + ep^2*r4[xi, w/w0]^2];  Plot[  ellgain[1.05, w, 1, 0.5],  {w, 0, 3}]  

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