D[InverseJacobiCN[z, m], {m, 3}] == (-(1/(8 (-1 + m)^3 m^3))) ((8 + 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiCN[z, m], m], m] + (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiCN[z, m], m], m] + 15 (-1 + m)^3 InverseJacobiCN[z, m] - (1/(1 + m (-1 + z^2))^(7/2)) ((-m) (-1 + z^2) z ((-1 + m) (1 + m (-1 + z^2))^3 JacobiNS[InverseJacobiCN[z, m], m] + ((-1 + m)^2 (5 + m (-13 + 23 m)) - (-1 + m) m (11 + m (-37 + 46 m)) z^2 + m^2 (9 + m (-24 + 23 m)) z^4) Sqrt[1 + m (-1 + z^2)] JacobiDS[InverseJacobiCN[z, m], m])))

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2007-05-02