InverseJacobiCN[z, m] == InverseJacobiCN[Subscript[z, 0], m] - ((Sqrt[1 - z^2] JacobiDS[InverseJacobiCN[z, m], m])/ Sqrt[1 + m (-1 + z^2)]) ((Sqrt[(-1 + m - m z^2)/(-1 + m)]/ Sqrt[1 - m + m z^2]) EllipticF[ArcSin[z], m/(-1 + m)] - (Sqrt[(-1 + m - m Subscript[z, 0]^2)/(-1 + m)]/ Sqrt[1 - m + m Subscript[z, 0]^2]) EllipticF[ArcSin[Subscript[z, 0]], m/(-1 + m)]) /; !Exists[\[Tau], {Element[\[Tau], Reals], 0 < \[Tau] < 1}, Im[1 - (Subscript[z, 0] + \[Tau] (z - Subscript[z, 0]))^2] == 0 && 1 - (Subscript[z, 0] + \[Tau] (z - Subscript[z, 0]))^2 < 0 && Im[m (Subscript[z, 0] + \[Tau] (z - Subscript[z, 0]))^2 - m + 1] == 0 && m (Subscript[z, 0] + \[Tau] (z - Subscript[z, 0]))^2 - m + 1 < 0]

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2007-05-02