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JacobiCD




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.25.27.0024.02









  


  








Input Form





JacobiCD[z, m] == EllipticTheta[2, (z Pi)/(2 EllipticK[m]), EllipticNomeQ[m]]/ EllipticTheta[3, (z Pi)/(2 EllipticK[m]), EllipticNomeQ[m]]/m^4^(-1)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiCD", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["m", RowBox[List[RowBox[List["-", "1"]], "/", "4"]]], FractionBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", FractionBox[RowBox[List["z", " ", "\[Pi]"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", FractionBox[RowBox[List["z", " ", "\[Pi]"]], 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> cd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mroot> <mi> m </mi> <mn> 4 </mn> </mroot> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mi> &#960; </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> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mi> &#960; </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> JacobiCD </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <ci> z </ci> <pi /> <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'> 3 </cn> <apply> <times /> <ci> z </ci> <pi /> <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["JacobiCD", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["m", RowBox[List[RowBox[List["-", "1"]], "/", "4"]]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", FractionBox[RowBox[List["z", " ", "\[Pi]"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]], RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", FractionBox[RowBox[List["z", " ", "\[Pi]"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]]]]]


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





2001-10-29