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http://functions.wolfram.com/09.18.03.0002.01
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WeierstrassHalfPeriods[{1, 0}] == {(1/(4 Sqrt[Pi])) Gamma[1/4]^2,
(I/(4 Sqrt[Pi])) Gamma[1/4]^2}
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List["1", ",", "0"]], "}"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["4", " ", SqrtBox["\[Pi]"]]]], SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], ",", RowBox[List[FractionBox["\[ImaginaryI]", RowBox[List["4", " ", SqrtBox["\[Pi]"]]]], SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]]]], "}"]]]]]]
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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> 1 </mn> <mo> , </mo> <mn> 0 </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> 1 </mn> <mo> , </mo> <mn> 0 </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> <msqrt> <mi> π </mi> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> ⅈ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </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'> 1 </cn> <cn type='integer'> 0 </cn> </apply> <apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> </apply> </list> <list> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </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["1", ",", "0"]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"], RowBox[List["4", " ", SqrtBox["\[Pi]"]]]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["4", " ", SqrtBox["\[Pi]"]]]]]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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