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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Identities involving the group of functions > Identities involving transformation of nome q > Algebraic addition theorems involving q2





http://functions.wolfram.com/09.01.18.0162.01









  


  








Input Form





EllipticTheta[3, x, q] EllipticTheta[3, y, q] == EllipticTheta[3, x + y, q^2] EllipticTheta[3, x - y, q^2] + EllipticTheta[2, x + y, q^2] EllipticTheta[2, x - y, q^2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "x", ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "y", ",", "q"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", RowBox[List["x", "+", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", RowBox[List["x", "-", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", RowBox[List["x", "+", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", RowBox[List["x", "-", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> y </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> - </mo> <mi> y </mi> </mrow> <mo> , </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> + </mo> <mi> y </mi> </mrow> <mo> , </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> - </mo> <mi> y </mi> </mrow> <mo> , </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> + </mo> <mi> y </mi> </mrow> <mo> , </mo> <msup> <mi> q </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> x </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> y </ci> <ci> q </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> x </ci> <ci> y </ci> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> y </ci> </apply> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> x </ci> <ci> y </ci> </apply> <apply> <power /> <ci> q </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "x_", ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "y_", ",", "q_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", RowBox[List["x", "+", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", RowBox[List["x", "-", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", RowBox[List["x", "+", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", RowBox[List["x", "-", "y"]], ",", SuperscriptBox["q", "2"]]], "]"]]]]]]]]]]


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





2001-10-29