Subscript[\[Eta], i] + Subscript[\[Omega], i] Subscript[e, j] == (Pi^2/(2 Subscript[\[Omega], i])) Sum[Sec[Pi ((2 n - 1)/2) (Subscript[\[Omega], k]/Subscript[\[Omega], i])]^ 2, {n, 1, Infinity}] /; Element[{i, j, k}, {1, 2, 3}] && i != j != k

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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> <msub> <mi> &#951; </mi> <mi> i </mi> </msub> <mo> + </mo> <mrow> <msub> <mi> e </mi> <mi> j </mi> </msub> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mi> i </mi> </msub> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mi> i </mi> </msub> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <msup> <mi> sec </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mfrac> <msub> <mi> &#969; </mi> <mi> k </mi> </msub> <msub> <mi> &#969; </mi> <mi> i </mi> </msub> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> i </mi> <mo> , </mo> <mi> j </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> i </mi> <mo> &#8800; </mo> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <ci> i </ci> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> j </ci> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> i </ci> </apply> </apply> </apply> <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> &#969; </ci> <ci> i </ci> </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> <power /> <apply> <sec /> <apply> <times /> <pi /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> i </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <list> <ci> i </ci> <ci> j </ci> <ci> k </ci> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> <apply> <neq /> <ci> i </ci> <ci> j </ci> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[Eta]_", "i_"], "+", RowBox[List[SubscriptBox["\[Omega]_", "i_"], " ", SubscriptBox["e_", "j"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], ")"]], " ", SubscriptBox["\[Omega]", "k"]]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "i"]]]], "]"]], "2"]]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "i"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j", ",", "k"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List["i", "\[NotEqual]", "j", "\[NotEqual]", "k"]]]]]]]]]]

2001-10-29