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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[z,{g2,g3}] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/09.15.04.0003.01









  


  








Input Form





WeierstrassSigma[Conjugate[z], {Conjugate[Subscript[g, 2]], Conjugate[Subscript[g, 3]]}] == Conjugate[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List["Conjugate", "[", "z", "]"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", SubscriptBox["g", "2"], "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["g", "3"], "]"]]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mover> <mi> z </mi> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mover> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[OverscriptBox[&quot;z&quot;, &quot;_&quot;], &quot;;&quot;, TagBox[OverscriptBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot;_&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[OverscriptBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], &quot;_&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mover> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mover> <mi> z </mi> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mover> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[OverscriptBox[&quot;z&quot;, &quot;_&quot;], &quot;;&quot;, TagBox[OverscriptBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot;_&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[OverscriptBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], &quot;_&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mover> <mrow> <mi> &#963; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List["Conjugate", "[", "z_", "]"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", SubscriptBox["g_", "2"], "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["g_", "3"], "]"]]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Conjugate", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "]"]]]]]]


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





2001-10-29