RamificationIndex[InverseJacobiCN[z, m], z, Sqrt[(-1 + m)/m]] == 2

Cell[BoxData[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["InverseJacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "z", ",", SqrtBox[FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", "m"]], "m"]]]], "]"]], "\[Equal]", "2"]]]]

<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> z </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> <msqrt> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </mfrac> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8475; </ci> <ci> z </ci> </apply> <apply> <ci> InverseJacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </math>

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

2001-10-29