D[InverseJacobiNC[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiNC[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiNC[z, m], m], m] + (1/(-m + (-1 + m) z^2)^3) (-15 (-1 + m)^3 (-m + (-1 + m) z^2)^3 InverseJacobiNC[z, m] + (1/z) (m ((-z^2 + m (-1 + z^2)) (5 z^4 + 23 m^4 (-1 + z^2)^2 + m^3 (-24 + 83 z^2 - 59 z^4) + m (11 z^2 - 23 z^4) + m^2 (9 - 48 z^2 + 54 z^4)) + (1 - m) Sqrt[1 + m (-1 + 1/z^2)] z (m + z^2 - m z^2)^3 JacobiCD[InverseJacobiNC[z, m], m]) JacobiSD[InverseJacobiNC[z, m], m])))

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2007-05-02