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http://functions.wolfram.com/09.20.08.0005.01
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(Subscript[e, 2] - Subscript[e, 3]) (Subscript[e, 1] - Subscript[e, 3])
(Subscript[e, 1] - Subscript[e, 2]) == (Pi^6/(4 Subscript[\[Omega], 1]^6))
q Product[1 - q^(2 n), {n, 1, Infinity}]^12
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e", "2"], "-", SubscriptBox["e", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "2"]]], ")"]]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "6"], RowBox[List["4", SubsuperscriptBox["\[Omega]", "1", "6"]]]], " ", "q", " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", "n"]]]]], ")"]]]], ")"]], "12"]]]]]]]
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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> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <msup> <mi> π </mi> <mn> 6 </mn> </msup> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 6 </mn> </msubsup> </mrow> </mfrac> <mo> ⁢ </mo> <mi> q </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 12 </mn> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> q </ci> <apply> <power /> <apply> <product /> <bvar> <ci> n </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 12 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e_", "2"], "-", SubscriptBox["e_", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["e_", "1"], "-", SubscriptBox["e_", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["e_", "1"], "-", SubscriptBox["e_", "2"]]], ")"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "6"], " ", "q", " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", " ", "n"]]]]], ")"]]]], ")"]], "12"]]], RowBox[List["4", " ", SubsuperscriptBox["\[Omega]", "1", "6"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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