InverseJacobiDC[z, m] == ((Sqrt[z^2 - m] JacobiSN[InverseJacobiDC[z, m], m])/ Sqrt[z^2 - 1]) Integrate[1/(Sqrt[t^2 - 1] Sqrt[t^2 - m]), {t, 1, z}] /; !Exists[\[Tau], {Element[\[Tau], Reals], 0 < \[Tau] < 1}, Im[(1 + \[Tau] (z - 1))^2 - 1] == 0 && (1 + \[Tau] (z - 1))^2 - 1 < 0 && Im[(1 + \[Tau] (z - 1))^2 - m] == 0 && (1 + \[Tau] (z - 1))^2 - m < 0]

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2007-05-02