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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Representations through equivalent functions > With related functions > Involving Jacobi functions





http://functions.wolfram.com/09.01.27.0018.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[FractionBox[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "z", ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["m", " ", RowBox[List["(", RowBox[List["1", "-", "m"]], ")"]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["JacobiSD", "[", 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> 1 </mn> </msub> <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> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <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> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mroot> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> sd </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'> <apply> <eq /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> z </ci> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> z </ci> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <ci> m </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ci> JacobiSD </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <ci> z </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z_", ",", RowBox[List["EllipticNomeQ", "[", "m_", "]"]]]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "z_", ",", RowBox[List["EllipticNomeQ", "[", "m_", "]"]]]], "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["m", " ", RowBox[List["(", RowBox[List["1", "-", "m"]], ")"]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["JacobiSD", "[", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]], " ", "z"]], "\[Pi]"], ",", "m"]], "]"]]]]]]]]


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





2007-05-02