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http://functions.wolfram.com/09.19.21.0001.01
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Integrate[WeierstrassInvariants[{Subscript[\[Omega], 1],
Subscript[\[Omega], 3]}], Subscript[\[Omega], 1]] ==
{-(Pi^4/(36 Subscript[\[Omega], 1]^3)) +
((5 Subscript[\[Omega], 1])/(2 Subscript[\[Omega], 3]^3))
Sum[(m^2 Subscript[\[Omega], 1]^2 + 3 m n Subscript[\[Omega], 1]
Subscript[\[Omega], 3] + 3 n^2 Subscript[\[Omega], 3]^2)/
(n^3 (m Subscript[\[Omega], 1] + n Subscript[\[Omega], 3])^3),
{m, -Infinity, Infinity}, {n, 1, Infinity}],
-(Pi^6/(1080 Subscript[\[Omega], 1]^5)) +
((7 Subscript[\[Omega], 1])/(8 Subscript[\[Omega], 3]^5))
Sum[(m^4 Subscript[\[Omega], 1]^4 + 5 m^3 n Subscript[\[Omega], 1]^3
Subscript[\[Omega], 3] + 10 m^2 n^2 Subscript[\[Omega], 1]^2
Subscript[\[Omega], 3]^2 + 10 m n^3 Subscript[\[Omega], 1]
Subscript[\[Omega], 3]^3 + 5 n^4 Subscript[\[Omega], 3]^4)/
(n^5 (m Subscript[\[Omega], 1] + n Subscript[\[Omega], 3])^5),
{m, -Infinity, Infinity}, {n, 1, Infinity}]}
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "]"]], RowBox[List["\[DifferentialD]", SubscriptBox["\[Omega]", "1"]]]]]]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "4"], RowBox[List["36", " ", SubsuperscriptBox["\[Omega]", "1", "3"]]]]]], "+", RowBox[List[FractionBox[RowBox[List["5", " ", SubscriptBox["\[Omega]", "1"]]], RowBox[List["2", SubsuperscriptBox["\[Omega]", "3", "3"]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List[SuperscriptBox["m", "2"], " ", SubsuperscriptBox["\[Omega]", "1", "2"]]], "+", RowBox[List["3", " ", "m", " ", "n", " ", SubscriptBox["\[Omega]", "1"], " ", SubscriptBox["\[Omega]", "3"]]], "+", RowBox[List["3", " ", SuperscriptBox["n", "2"], " ", SubsuperscriptBox["\[Omega]", "3", "2"]]]]], RowBox[List[SuperscriptBox["n", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], "3"]]]]]]]]]]]], ",", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "6"], RowBox[List["1080", " ", SubsuperscriptBox["\[Omega]", "1", "5"]]]]]], "+", RowBox[List[FractionBox[RowBox[List["7", " ", SubscriptBox["\[Omega]", "1"]]], RowBox[List["8", " ", SubsuperscriptBox["\[Omega]", "3", "5"]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["m", "4"], " ", SubsuperscriptBox["\[Omega]", "1", "4"]]], "+", RowBox[List["5", " ", SuperscriptBox["m", "3"], " ", "n", " ", SubsuperscriptBox["\[Omega]", "1", "3"], " ", SubscriptBox["\[Omega]", "3"]]], "+", RowBox[List["10", " ", SuperscriptBox["m", "2"], " ", SuperscriptBox["n", "2"], " ", SubsuperscriptBox["\[Omega]", "1", "2"], " ", SubsuperscriptBox["\[Omega]", "3", "2"]]], "+", RowBox[List["10", " ", "m", " ", SuperscriptBox["n", "3"], " ", SubscriptBox["\[Omega]", "1"], " ", SubsuperscriptBox["\[Omega]", "3", "3"]]], "+", RowBox[List["5", " ", SuperscriptBox["n", "4"], " ", SubsuperscriptBox["\[Omega]", "3", "4"]]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox["n", "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], "5"]]], ")"]]]]]]]]]]]]]], "}"]]]]]]
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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> <mo> ∫ </mo> <mrow> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mrow> <mo> , </mo> <mrow> <mo> ∫ </mo> <mrow> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mrow> </mrow> <mo> } </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mfrac> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> m </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> </mrow> <mi> ∞ </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <mrow> <mrow> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> n </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mrow> <msup> <mi> n </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> - </mo> <mfrac> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mfrac> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 3 </mn> <mn> 5 </mn> </msubsup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> m </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> </mrow> <mi> ∞ </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> m </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> n </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <msup> <mi> n </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msup> <mi> n </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 3 </mn> <mn> 4 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> n </mi> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <mfrac> <msup> <mi> π </mi> <mn> 6 </mn> </msup> <mrow> <mn> 1080 </mn> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 5 </mn> </msubsup> </mrow> </mfrac> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <list> <apply> <int /> <bvar> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <int /> <bvar> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> n </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> m </ci> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> n </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> n </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> n </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1080 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </list> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]_", "1"], ",", SubscriptBox["\[Omega]_", "3"]]], "}"]], "]"]], RowBox[List["\[DifferentialD]", SubscriptBox["\[Omega]_", "1"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "4"], RowBox[List["36", " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "3"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["5", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List[SuperscriptBox["m", "2"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]], "+", RowBox[List["3", " ", "m", " ", "n", " ", SubscriptBox["\[Omega]\[Omega]", "1"], " ", SubscriptBox["\[Omega]\[Omega]", "3"]]], "+", RowBox[List["3", " ", SuperscriptBox["n", "2"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "3", "2"]]]]], RowBox[List[SuperscriptBox["n", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["m", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], "+", RowBox[List["n", " ", SubscriptBox["\[Omega]\[Omega]", "3"]]]]], ")"]], "3"]]]]]]]]]], RowBox[List["2", " ", SubsuperscriptBox["\[Omega]\[Omega]", "3", "3"]]]]]], ",", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "6"], RowBox[List["1080", " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "5"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["7", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List[SuperscriptBox["m", "4"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "4"]]], "+", RowBox[List["5", " ", SuperscriptBox["m", "3"], " ", "n", " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "3"], " ", SubscriptBox["\[Omega]\[Omega]", "3"]]], "+", RowBox[List["10", " ", SuperscriptBox["m", "2"], " ", SuperscriptBox["n", "2"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "3", "2"]]], "+", RowBox[List["10", " ", "m", " ", SuperscriptBox["n", "3"], " ", SubscriptBox["\[Omega]\[Omega]", "1"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "3", "3"]]], "+", RowBox[List["5", " ", SuperscriptBox["n", "4"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "3", "4"]]]]], RowBox[List[SuperscriptBox["n", "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["m", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], "+", RowBox[List["n", " ", SubscriptBox["\[Omega]\[Omega]", "3"]]]]], ")"]], "5"]]]]]]]]]], RowBox[List["8", " ", SubsuperscriptBox["\[Omega]\[Omega]", "3", "5"]]]]]]]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
