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JacobiDC




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDC[z,m] > Transformations > Transformations and argument simplifications > Argument involving inverse Jacobi functions





http://functions.wolfram.com/09.28.16.0043.01









  


  








Input Form





JacobiDC[InverseJacobiSN[z, m], m]^2 == (m z^2 - 1)/(z^2 - 1)








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["JacobiDC", "[", RowBox[List[RowBox[List["InverseJacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], "2"], "\[Equal]", FractionBox[RowBox[List[RowBox[List["m", " ", SuperscriptBox["z", "2"]]], "-", "1"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]]]








MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["JacobiDC", "[", RowBox[List[RowBox[List["InverseJacobiSN", "[", RowBox[List["z_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["m", " ", SuperscriptBox["z", "2"]]], "-", "1"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02