JacobiDN[InverseJacobiSD[z, m], m]^2 == 1/(1 + m z^2)

Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["InverseJacobiSD", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], "2"], "\[Equal]", FractionBox["1", RowBox[List["1", "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> sd </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> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#63449; </mo> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <ci> JacobiDN </ci> <apply> <ci> InverseJacobiSD </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List[RowBox[List["InverseJacobiSD", "[", RowBox[List["z_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["1", "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]]]]]]]

2007-05-02