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http://functions.wolfram.com/09.17.06.0006.01
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WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2],
Subscript[g, 3]}] == (-Subscript[e, 1]) Subscript[\[Omega], 1] +
(Pi^2/(2 Subscript[\[Omega], 1]))
(1/2 + 4 Sum[q^(2 k)/(1 + q^(2 k))^2, {k, 1, Infinity}])
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Cell[BoxData[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["e", "1"]]], SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], " ", RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["4", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox["q", RowBox[List["2", "k"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["q", RowBox[List["2", "k"]]]]], ")"]], "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> <msub> <mi> η </mi> <mn> 1 </mn> </msub> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <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["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["e", "1"]]], " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox["q", RowBox[List["2", " ", "k"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["q", RowBox[List["2", " ", "k"]]]]], ")"]], "2"]]]]]]]], ")"]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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