RamificationIndex[InverseJacobiCN[z, m], m, 1/(1 - z^2)] == Log

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#8475; </mi> <mi> m </mi> </msub> <mo> ( </mo> <mrow> <mrow> <msup> <mi> cn </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mi> log </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8475; </ci> <ci> m </ci> </apply> <apply> <ci> InverseJacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> log </ci> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], ",", "m_", ",", FractionBox["1", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]]]], "]"]], "]"]], "\[RuleDelayed]", "Log"]]]]

2001-10-29