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http://functions.wolfram.com/09.18.03.0003.01
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WeierstrassHalfPeriods[{0, 1}] == {(1/(4 Pi)) Gamma[1/3]^3,
((1 + Sqrt[3] I)/(8 Pi)) Gamma[1/3]^3}
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["4", " ", "\[Pi]"]]], SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], "3"]]], ",", RowBox[List[FractionBox[RowBox[List["1", "+", RowBox[List[SqrtBox["3"], " ", "\[ImaginaryI]"]]]], RowBox[List["8", " ", "\[Pi]"]]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], "3"]]]]], "}"]]]]]]
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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> <mrow> <mo> { </mo> <mrow> <mrow> <mstyle scriptlevel='0'> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mstyle scriptlevel='0'> <mo> , </mo> </mstyle> <mrow> <mstyle scriptlevel='0'> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> </mrow> <mstyle scriptlevel='0'> <mo> } </mo> </mstyle> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> , </mo> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <list> <apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </apply> <apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </list> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], "3"], RowBox[List["4", " ", "\[Pi]"]]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List[SqrtBox["3"], " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]], "3"]]], RowBox[List["8", " ", "\[Pi]"]]]]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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