InverseJacobiCD[z, m] == InverseJacobiCD[Subscript[z, 0], m] - ((Sqrt[1 - m z^2] JacobiSN[InverseJacobiCD[z, m], m])/Sqrt[1 - z^2]) Integrate[1/(Sqrt[1 - t^2] Sqrt[1 - m t^2]), {t, Subscript[z, 0], z}] /; !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[1 - m (Subscript[z, 0] + \[Tau] (z - Subscript[z, 0]))^2] == 0 && 1 - m (Subscript[z, 0] + \[Tau] (z - Subscript[z, 0]))^2 < 0]

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</mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mi> z </mi> </msubsup> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> t </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msup> <mi> t </mi> <mn> 2 </mn> </msup> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> &#172; </mo> <mrow> <msub> <mo> &#8707; </mo> <mrow> <mi> &#964; </mi> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mi> &#964; </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[List[], Reals]] </annotation> </semantics> </mrow> <mo> , </mo> <mrow> <mn> 0 </mn> <mo> &lt; 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2007-05-02