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JacobiCN




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiCN[z,m] > Representations through equivalent functions > With related functions > Involving theta functions





http://functions.wolfram.com/09.26.27.0026.02









  


  








Input Form





JacobiCN[z, m] == ((1 - m)^(1/4) (EllipticTheta[2, (Pi z)/(2 EllipticK[m]), EllipticNomeQ[m]]/EllipticTheta[4, (Pi z)/(2 EllipticK[m]), EllipticNomeQ[m]]))/m^4^(-1)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiCN", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "m"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["m", RowBox[List[RowBox[List["-", "1"]], "/", "4"]]], " ", FractionBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]]]]]]]








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> cn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> m </mi> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <mfrac> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiCN </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='rational'> -1 <sep /> 4 </cn> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiCN", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "m"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["m", RowBox[List[RowBox[List["-", "1"]], "/", "4"]]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]]]]]


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





2001-10-29