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JacobiCD




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiCD[z,m] > Representations through equivalent functions > With related functions > Involving am





http://functions.wolfram.com/09.25.27.0026.01









  


  








Input Form





JacobiCD[z, m]^2 == Cos[JacobiAmplitude[z, m]]^2/ (1 - m Sin[JacobiAmplitude[z, m]]^2)








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["JacobiCD", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], "\[Equal]", FractionBox[SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "]"]], "2"], RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "]"]], "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> cd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#63449; </mo> <mfrac> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <ci> JacobiCD </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <power /> <apply> <cos /> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <sin /> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </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["JacobiCD", "[", RowBox[List["z_", ",", "m_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "]"]], "2"], RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["JacobiAmplitude", "[", RowBox[List["z", ",", "m"]], "]"]], "]"]], "2"]]]]]]]]]]


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





2007-05-02