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JacobiND




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiND[z,m] > Transformations > Multiple arguments > Double angle formulas





http://functions.wolfram.com/09.32.16.0020.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiND", "[", RowBox[List[RowBox[List["2", "z"]], ",", "m"]], "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], "-", " ", RowBox[List[SuperscriptBox[RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], "-", "1"]], ")"]]]]]], RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], "+", " ", RowBox[List[SuperscriptBox[RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["JacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "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> <mrow> <mi> nd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mrow> <mi> dn </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> - </mo> <mrow> <msup> <mrow> <mi> cn </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> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mi> dn </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> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mi> dn </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> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mi> cn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msup> <mrow> <mi> dn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiND </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <ci> JacobiDN </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29