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http://functions.wolfram.com/09.04.13.0002.01
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(30 Derivative[1][w][\[Tau]]^3 - 15 w[\[Tau]] Derivative[1][w][\[Tau]]
Derivative[2][w][\[Tau]] + w[\[Tau]]^2 Derivative[3][w][\[Tau]])^2 -
32 (3 Derivative[1][w][\[Tau]]^2 - w[\[Tau]] Derivative[2][w][\[Tau]])^3 +
Pi^2 w[\[Tau]]^10 (w[\[Tau]] Derivative[2][w][\[Tau]] -
3 Derivative[1][w][\[Tau]]^2)^2 == 0 /;
w[\[Tau]] == EllipticTheta[4, 0, E^(I Pi \[Tau])]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["30", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]], "3"]]], "-", RowBox[List["15", " ", RowBox[List["w", "[", "\[Tau]", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["w", "[", "\[Tau]", "]"]], "2"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]]]]]], ")"]], "2"], "-", RowBox[List["32", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]], "2"]]], "-", RowBox[List[RowBox[List["w", "[", "\[Tau]", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]]]]]], ")"]], "3"]]], "+", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["w", "[", "\[Tau]", "]"]], "10"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["w", "[", "\[Tau]", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]]]], "-", RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]", "]"]], "2"]]]]], ")"]], "2"]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", "\[Tau]", "]"]], "\[Equal]", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]], "]"]]]]]]]]
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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> <mrow> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", "3", ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> τ </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> τ </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <ci> w </ci> <ci> τ </ci> </apply> <apply> <partialdiff /> <bvar> <ci> τ </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> τ </ci> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> w </ci> <ci> τ </ci> </apply> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> τ </ci> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> w </ci> <ci> τ </ci> </apply> <apply> <partialdiff /> <bvar> <ci> τ </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> τ </ci> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <ci> w </ci> <ci> τ </ci> </apply> <apply> <partialdiff /> <bvar> <ci> τ </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> τ </ci> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> w </ci> <ci> τ </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> τ </ci> <degree> <cn type='integer'> 3 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> τ </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> τ </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 0 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> τ </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["30", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]], "3"]]], "-", RowBox[List["15", " ", RowBox[List["w", "[", "\[Tau]_", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["w", "[", "\[Tau]_", "]"]], "2"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]]]]]], ")"]], "2"], "-", RowBox[List["32", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]], "2"]]], "-", RowBox[List[RowBox[List["w", "[", "\[Tau]_", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]]]]]], ")"]], "3"]]], "+", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["w", "[", "\[Tau]_", "]"]], "10"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["w", "[", "\[Tau]_", "]"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]]]], "-", RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Tau]_", "]"]], "2"]]]]], ")"]], "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "\[Tau]", "]"]], "\[Equal]", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Tau]"]]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
