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CarlsonRG

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Carlson symmetric elliptic integral of the second kind R_G

CarlsonRG[x, y, z]
CarlsonRG[3., 5., 11.] → 2.4807804428774662 Sin[ϕ]CarlsonRG[Cos[ϕ]^2, 1 - m Sin[ϕ]^2, 1] /. {m -> 0.3, ϕ -> Pi / 5.} → 1.08238725326179Plot[{CarlsonRG[t, 2, 3], CarlsonRG[1, t, 3], CarlsonRG[1, 2, t]}, {t, 0, 6}, PlotLegends -> "Expressions"] → -Graphics-

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