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http://functions.wolfram.com/09.16.03.0008.01
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WeierstrassSigma[i, Subscript[\[Omega], k], {Subscript[g, 2],
Subscript[g, 3]}]/(WeierstrassSigma[i, Subscript[\[Omega], j],
{Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[k,
Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}]) ==
Exp[Subscript[\[Eta], j] Subscript[\[Omega], i]] /;
Element[{i, j, k}, {1, 2, 3}] && i != j != k
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", SubscriptBox["\[Omega]", "k"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "/", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", SubscriptBox["\[Omega]", "j"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", SubscriptBox["\[Omega]", "i"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]]]], "\[Equal]", RowBox[List["Exp", "[", RowBox[List[SubscriptBox["\[Eta]", "j"], " ", SubscriptBox["\[Omega]", "i"]]], "]"]]]], "/;", 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", "\[NotEqual]", "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> <mfrac> <mrow> <msub> <mi> σ </mi> <mi> i </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <msub> <mi> ω </mi> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["\[Omega]", "k"], Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "2"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "3"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <msub> <mi> σ </mi> <mi> i </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <msub> <mi> ω </mi> <mi> j </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["\[Omega]", "j"], Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "2"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "3"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> σ </mi> <mi> k </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <msub> <mi> ω </mi> <mi> i </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["\[Omega]", "i"], Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "2"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox["g", "3"], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⩵ </mo> <msup> <mi> ⅇ </mi> <mrow> <msub> <mi> η </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mi> i </mi> </msub> </mrow> </msup> </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> ∈ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> i </mi> <mo> ≠ </mo> <mi> j </mi> <mo> ≠ </mo> <mi> k </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> σ </ci> <ci> i </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <ci> k </ci> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> σ </ci> <ci> i </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <ci> j </ci> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> σ </ci> <ci> k </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <ci> i </ci> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> η </ci> <ci> j </ci> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <ci> i </ci> </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>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", SubscriptBox["\[Omega]_", "k"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", SubscriptBox["\[Omega]_", "j"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", SubscriptBox["\[Omega]_", "i_"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SubscriptBox["\[Eta]", "j"], " ", 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"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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