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http://functions.wolfram.com/09.17.27.0008.01
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WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}]^
2 == (Subscript[g, 2]/6 - Subscript[e, i]^2) Subscript[\[Omega], 1]^2 -
((Pi^2 Subscript[\[Eta], 1])/(2 Subscript[\[Omega], 1]))
(Derivative[0, 2, 0][EllipticTheta][i + 1, 0, q]/
EllipticTheta[i + 1, 0, q]) - (Pi^4/(48 Subscript[\[Omega], 1]^2))
(Derivative[0, 4, 0][EllipticTheta][i + 1, 0, q]/
EllipticTheta[i + 1, 0, q]) /; Element[i, {1, 2, 3}]
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Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[SubscriptBox["g", "2"], "6"], "-", SubsuperscriptBox["e", "i", "2"]]], ")"]], " ", SubsuperscriptBox["\[Omega]", "1", "2"]]], "-", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], SubscriptBox["\[Eta]", "1"]]], RowBox[List["2", SubscriptBox["\[Omega]", "1"]]]], " ", FractionBox[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "2", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]], "-", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "4"], RowBox[List["48", SubsuperscriptBox["\[Omega]", "1", "2"]]]], " ", FractionBox[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "4", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]
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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> <msubsup> <mi> η </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mn> 6 </mn> </mfrac> <mo> - </mo> <msubsup> <mi> e </mi> <mi> i </mi> <mn> 2 </mn> </msubsup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <msub> <mi> e </mi> <mi> i </mi> </msub> <mo> - </mo> <mrow> <mfrac> <mrow> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msub> <mi> η </mi> <mn> 1 </mn> </msub> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ⁢ </mo> <mfrac> <mrow> <msubsup> <mi> ϑ </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ″ </mo> </msubsup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> ϑ </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> </mfrac> </mrow> <mo> - </mo> <mrow> <mfrac> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mrow> <mn> 48 </mn> <mo> ⁢ </mo> <msubsup> <mi> ω </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </mfrac> <mo> ⁢ </mo> <mfrac> <mrow> <msubsup> <mi> ϑ </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> ϑ </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> </mfrac> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> i </mi> <mo> ∈ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> i </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> i </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> η </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 2 </cn> </list> <apply> <ci> Subscript </ci> <ci> ϑ </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </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'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> ϑ </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </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'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> i </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[SubscriptBox["gg", "2"], "6"], "-", SubsuperscriptBox["e", "i", "2"]]], ")"]], " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SubscriptBox["\[Eta]", "1"]]], ")"]], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "2", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "4"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "4", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["48", " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List[RowBox[List["i", "+", "1"]], ",", "0", ",", "q"]], "]"]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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