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JacobiND




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.32.16.0042.01









  


  








Input Form





JacobiND[InverseJacobiNC[z, m], m]^2 == z^2/((1 - m) z^2 + m)








Standard Form





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








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> nd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> nc </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> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mi> m </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <ci> JacobiND </ci> <apply> <ci> InverseJacobiNC </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> m </ci> </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["JacobiND", "[", RowBox[List[RowBox[List["InverseJacobiNC", "[", RowBox[List["z_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["z", "2"], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "m"]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", "m"]]]]]]]


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





2007-05-02