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JacobiNC




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.31.16.0050.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["JacobiNC", "[", RowBox[List[RowBox[List["InverseJacobiSD", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], "2"], "\[Equal]", FractionBox[RowBox[List["1", "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]], RowBox[List["1", "+", RowBox[List[RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", SuperscriptBox["z", "2"]]]]]]]]]]








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> nc </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> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> JacobiNC </ci> <apply> <ci> InverseJacobiSD </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> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <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>










Rule Form





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


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





2007-05-02