D[InverseJacobiSD[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiSD[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiSD[z, m], m], m] + (-15 (-1 + m + (-1 + m)^2 z^2)^3 (1 + m z^2)^2 InverseJacobiSD[z, m] + m JacobiCN[InverseJacobiSD[z, m], m] ((-(-1 + m)) m z (6 + 2 (-9 + 19 m) z^2 + (13 - 69 m + 78 m^2) z^4 + (-1 + m (23 - 80 m + 66 m^2)) z^6 + (-1 + m) m (-2 + m (-9 + 20 m)) z^8) + (1 + m z^2) ((-(-1 + m)) (1 + (-1 + m) z^2) Sqrt[1/(1 + m z^2)] (-1 + (-3 + 5 m) z^2 + (4 + m (-18 + 17 m)) z^4 + (-1 + m) m (-7 + 11 m) z^6) + (5 - 18 m + 21 m^2 + 2 (-5 + m (32 + m (-73 + 54 m))) z^2 + (5 + m (-58 + m (231 - 376 m + 206 m^2))) z^4 + 2 (-1 + m) m (-6 + m (43 + m (-109 + 86 m))) z^6 + (-1 + m)^2 m^2 (7 + m (-36 + 53 m)) z^8) JacobiDN[InverseJacobiSD[z, m], m]) JacobiSN[InverseJacobiSD[z, m], m]))/((1 + (-1 + m) z^2)^3 (1 + m z^2)^2))

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2007-05-02