WeierstrassSigma[2, Subscript[\[Omega], 3], {Subscript[g, 2], Subscript[g, 3]}] == 2 q^(1/4) Exp[(Subscript[\[Eta], 3] Subscript[\[Omega], 3])/2] Product[(1 + q^(2 n))/(1 + q^(2 n - 1)), {n, 1, Infinity}]^2

Cell[BoxData[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["2", ",", SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["2", SuperscriptBox["q", RowBox[List["1", "/", "4"]]], RowBox[List["Exp", "[", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "3"], " ", SubscriptBox["\[Omega]", "3"]]], "2"], "]"]], " ", SuperscriptBox[RowBox[List["(", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["1", "+", SuperscriptBox["q", RowBox[List["2", "n"]]]]], RowBox[List["1", "+", SuperscriptBox["q", RowBox[List[RowBox[List["2", "n"]], "-", "1"]]]]]]]], ")"]], "2"]]]]]]]

<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> &#963; </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#969; </mi> <mn> 3 </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[&quot;\[Sigma]&quot;, &quot;2&quot;], &quot;(&quot;, RowBox[List[RowBox[List[TagBox[SubscriptBox[&quot;\[Omega]&quot;, &quot;3&quot;], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mroot> <mi> q </mi> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> exp </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <msub> <mi> &#951; </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mtext> </mtext> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> q </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </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> &#969; </ci> <cn type='integer'> 3 </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 /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> q </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <exp /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </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> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["2", ",", SubscriptBox["\[Omega]_", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", SuperscriptBox["q", RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SubscriptBox["\[Eta]", "3"], " ", SubscriptBox["\[Omega]\[Omega]", "3"]]], "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["1", "+", SuperscriptBox["q", RowBox[List["2", " ", "n"]]]]], RowBox[List["1", "+", SuperscriptBox["q", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]]]]]]]], ")"]], "2"]]]]]]]

2001-10-29