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JacobiNC




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiNC[z,m] > Transformations > Half-angle formulas





http://functions.wolfram.com/09.31.16.0018.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["JacobiNC", "[", RowBox[List[FractionBox["z", "2"], ",", "m"]], "]"]], "2"], "\[Equal]", FractionBox[RowBox[List["1", "+", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "+", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "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> nc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#10869; </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> cn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <ci> JacobiNC </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </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["JacobiNC", "[", RowBox[List[FractionBox["z_", "2"], ",", "m_"]], "]"]], "2"], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["1", "+", RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "+", RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]]


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





2001-10-29