Subscript[\[Eta], 1] == Pi^2/(12 Subscript[\[Omega], 1]) - ((2 Pi^2)/Subscript[\[Omega], 1]) Sum[(k q^(2 k))/(1 - q^(2 k)), {k, 1, Infinity}]

Cell[BoxData[RowBox[List[SubscriptBox["\[Eta]", "1"], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["12", SubscriptBox["\[Omega]", "1"]]]], "-", RowBox[List[FractionBox[RowBox[List["2", SuperscriptBox["\[Pi]", "2"]]], SubscriptBox["\[Omega]", "1"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["k", " ", SuperscriptBox["q", RowBox[List["2", "k"]]]]], RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", "k"]]]]]]]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <mi> &#951; </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mfrac> <mrow> <mi> k </mi> <mo> &#8290; </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <ci> k </ci> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <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> k </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "1"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["12", " ", SubscriptBox["\[Omega]", "1"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["k", " ", SuperscriptBox["q", RowBox[List["2", " ", "k"]]]]], RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", " ", "k"]]]]]]]]]], SubscriptBox["\[Omega]", "1"]]]]]]]]

2001-10-29