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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[2,z,q] > Representations through equivalent functions > With related functions > Involving Jacobi functions





http://functions.wolfram.com/09.02.27.0008.02









  


  








Input Form





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








Standard Form





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








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mroot> <mrow> <mi> m </mi> <mtext> </mtext> </mrow> <mn> 4 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> &#8290; </mo> <mrow> <mi> cn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mi> &#960; </mi> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mfrac> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mroot> <mrow> <mi> m </mi> <mtext> </mtext> </mrow> <mn> 4 </mn> </mroot> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mn> 4 </mn> </mroot> </mfrac> <mo> &#8290; </mo> <mrow> <mi> cn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mi> &#960; </mi> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29