EllipticF[ArcSin[z], m] == (-(Sqrt[-z^2]/z)) (EllipticK[1 - m] + (1/2) (1 - (I Sqrt[-z^4])/z^2) I (1 - Sqrt[m] Sqrt[1/m]) EllipticK[m]) - ((Sqrt[1 - z^2] Sqrt[1 - m z^2])/(Sqrt[m] Sqrt[1 - 1/z^2] Sqrt[1 - 1/(m z^2)] z^2)) EllipticF[ArcSin[1/(Sqrt[m] z)], m]

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2007-05-02