D[InverseJacobiDN[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiDN[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiDN[z, m], m], m] + (1/(-1 + m + z^2)^3) (-15 (-1 + m)^3 (-1 + m + z^2)^3 InverseJacobiDN[z, m] + (-1 + m + z^2) (15 (-1 + m)^2 (1 + 3 (-1 + m) m) z + 5 (-1 + m) (6 + m (-17 + 15 m)) z^3 + (15 + m (-40 + 33 m)) z^5 - (-1 + m) (-7 + 10 m) z^4 Sqrt[z^2] - (-1 + m)^2 Sqrt[z^2] (7 - 18 m + 11 m^2 + 7 (-2 + 3 m) z^2)) JacobiSC[InverseJacobiDN[z, m], m]))

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2007-05-02