Subscript[e, j] - Subscript[e, k] == (Pi/(2 Subscript[\[Omega], 1]))^2 EllipticTheta[i + 1, 0, q]^4 /; Element[{i, j, k}, {1, 2, 3}] && Inequality[i, Unequal, j, Less, k]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["e", "j"], "-", SubscriptBox["e", "k"]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["\[Pi]", RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]], "4"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j", ",", "k"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "\[And]", RowBox[List["i", "\[NotEqual]", "j", "<", "k"]]]]]]]]

<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> e </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> e </mi> <mi> k </mi> </msub> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> &#960; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> &#977; </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </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> &lt; </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> e </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> k </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <cn type='integer'> 4 </cn> </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> <ci> Inequality </ci> <ci> i </ci> <neq /> <ci> j </ci> <lt /> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["e_", "j"], "-", SubscriptBox["e_", "k"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["\[Pi]", RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]], "4"]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j", ",", "k"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List["i", "\[NotEqual]", "j", "<", "k"]]]]]]]]]]

2001-10-29