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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[z,{g2,g3}] > Specific values > Values at fixed points





http://functions.wolfram.com/09.15.03.0013.01









  


  








Input Form





WeierstrassSigma[Subscript[\[Omega], 2], {1, 0}] == (-E^(Pi/4)) 2^(1/2) E^(I (Pi/4))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List["1", ",", "0"]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", "/", "4"]]]]], SuperscriptBox["2", RowBox[List["1", "/", "2"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["\[Pi]", "/", "4"]]]]]]]]]]]








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> <msub> <mi> &#969; </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Sigma]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[SubscriptBox[&quot;\[Omega]&quot;, &quot;2&quot;], Rule[Editable, True]], &quot;;&quot;, TagBox[&quot;1&quot;, Rule[Editable, True]]]], &quot;,&quot;, TagBox[&quot;0&quot;, Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#960; </mi> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 4 </mn> </mfrac> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WeierstrassSigma </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 2 </cn> </apply> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </list> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["\[Omega]_", "2"], ",", RowBox[List["{", RowBox[List["1", ",", "0"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Pi]", "/", "4"]]]]], " ", SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "4"]]]]]]]]


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





2001-10-29