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http://functions.wolfram.com/09.15.03.0015.01
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WeierstrassSigma[z, WeierstrassInvariants[{Subscript[\[Omega], 1],
ComplexInfinity}]] == ((2 Subscript[\[Omega], 1])/Pi)
Exp[(1/6) ((Pi z)/(2 Subscript[\[Omega], 1]))^2]
Sin[(Pi z)/(2 Subscript[\[Omega], 1])]
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", "ComplexInfinity"]], "}"]], "]"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", SubscriptBox["\[Omega]", "1"]]], "\[Pi]"], " ", RowBox[List["Exp", "[", RowBox[List[FractionBox["1", "6"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ")"]], "2"]]], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox["z", Rule[Editable, True]], ";", TagBox[RowBox[List[SubscriptBox["g", "2"], "(", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", OverscriptBox["\[Infinity]", "~"]]], ")"]], Rule[Editable, True]]]], ",", TagBox[RowBox[List[SubscriptBox["g", "3"], "(", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", OverscriptBox["\[Infinity]", "~"]]], ")"]], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WeierstrassSigma </ci> <ci> z </ci> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> </list> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <exp /> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <power /> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["z_", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]_", "1"], ",", "ComplexInfinity"]], "}"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "6"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]]], ")"]], "2"]]]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]]], "]"]]]], "\[Pi]"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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