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http://functions.wolfram.com/09.53.13.0001.01
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w[m]^2 (2 (m - 1)^2 Derivative[1][w][m] Derivative[3][w][m] m^2 -
3 (m - 1)^2 m^2 Derivative[2][w][m]^2 - (m^2 - m + 1)
Derivative[1][w][m]^2) + (m - 1)^2 m^2 Derivative[1][w][m]^4 == 0 /;
w[m] == EllipticNomeQ[m]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["w", "[", "m", "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], "2"], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "m", "]"]], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "m", "]"]], " ", SuperscriptBox["m", "2"]]], "-", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], "2"], " ", SuperscriptBox["m", "2"], " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "m", "]"]], "2"]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["m", "2"], "-", "m", "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "m", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], "2"], " ", SuperscriptBox["m", "2"], " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "m", "]"]], "4"]]]]], "\[Equal]", "0"]], " ", "/;", " ", RowBox[List[RowBox[List["w", "[", "m", "]"]], "\[Equal]", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]]]]]]
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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> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mi> ′′ </mi> </msup> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <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> m </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> w </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> w </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> m </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> w </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> m </ci> <degree> <cn type='integer'> 3 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> w </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> m </ci> </apply> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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