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http://functions.wolfram.com/09.16.08.0012.01
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WeierstrassSigma[1, Subscript[\[Omega], 2],
{Subscript[g, 2], Subscript[g, 3]}] == (-((I Sqrt[I])/(2 q^(1/4))))
E^((Subscript[\[Eta], 2] Subscript[\[Omega], 2])/2)
Product[(1 - q^(2 n - 1))/(1 + q^(2 n)), {n, 1, Infinity}]^2
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["1", ",", SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["\[ImaginaryI]"]]], RowBox[List["2", SuperscriptBox["q", RowBox[List["1", "/", "4"]]]]]]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "2"], " ", SubscriptBox["\[Omega]", "2"]]], "2"]], SuperscriptBox[RowBox[List["(", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["1", "-", SuperscriptBox["q", RowBox[List[RowBox[List["2", "n"]], "-", "1"]]]]], RowBox[List["1", "+", SuperscriptBox["q", RowBox[List["2", "n"]]]]]]]], ")"]], "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> <semantics> <mrow> <msub> <mi> σ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ω </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox["\[Sigma]", "1"], "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["\[Omega]", "2"], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mi> ⅈ </mi> </msqrt> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mroot> <mi> q </mi> <mn> 4 </mn> </mroot> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <msub> <mi> η </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 2 </mn> </msub> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> q </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </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> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <imaginaryi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> q </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <exp /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <product /> <bvar> <ci> n </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> q </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["1", ",", SubscriptBox["\[Omega]_", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox["\[ImaginaryI]"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "2"], " ", SubscriptBox["\[Omega]\[Omega]", "2"]]], "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["1", "-", SuperscriptBox["q", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]]]]], RowBox[List["1", "+", SuperscriptBox["q", RowBox[List["2", " ", "n"]]]]]]]], ")"]], "2"]]], RowBox[List["2", " ", SuperscriptBox["q", RowBox[List["1", "/", "4"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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