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http://functions.wolfram.com/09.15.03.0010.01
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WeierstrassSigma[Subscript[\[Omega], 2], {0, 1}] ==
E^(Pi/(4 Sqrt[3])) (2^(1/3)/3^(1/4)) E^(4 Pi (I/3))
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["\[Pi]", RowBox[List["4", SqrtBox["3"]]]]], " ", FractionBox[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], SuperscriptBox["3", RowBox[List["1", "/", "4"]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", "\[Pi]", " ", RowBox[List["\[ImaginaryI]", "/", "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> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ω </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mn> 0 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["\[Omega]", "2"], Rule[Editable, True]], ";", TagBox["0", Rule[Editable, True]]]], ",", TagBox["1", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <msup> <mi> ⅇ </mi> <mfrac> <mi> π </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <mfrac> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mroot> <mn> 3 </mn> <mn> 4 </mn> </mroot> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 3 </mn> </mfrac> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> WeierstrassSigma </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 2 </cn> </apply> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </list> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <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[SubscriptBox["\[Omega]_", "2"], ",", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["\[Pi]", RowBox[List["4", " ", SqrtBox["3"]]]]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["4", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "3"]]]], SuperscriptBox["3", RowBox[List["1", "/", "4"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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