Integrate[InverseJacobiCN[z, m], m] == 2 ((z Sqrt[1 + m (-1 + z^2)] - z)/Sqrt[1 - z^2] + I Sqrt[m] (EllipticE[I ArcSinh[Sqrt[m]/Sqrt[1 - m]], (m - 1)/m] - EllipticE[I ArcSinh[(Sqrt[m] z)/Sqrt[1 - m]], (m - 1)/m] - EllipticF[I ArcSinh[Sqrt[m]/Sqrt[1 - m]], (m - 1)/m] + EllipticF[I ArcSinh[(Sqrt[m] z)/Sqrt[1 - m]], (m - 1)/m])) /; z < 1 && 0 < m < 1

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2001-10-29