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DedekindEta




Mathematica Notation

Traditional Notation









Elliptic Functions > DedekindEta[z] > Differential equations > Ordinary nonlinear differential equations





http://functions.wolfram.com/09.49.13.0002.01









  


  








Input Form





Derivative[3][w][z] - 24 Derivative[2][w][z] w[z] + 36 Derivative[1][w][z]^2 == 0 /; w[z] == Derivative[1][DedekindEta][z]/DedekindEta[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["w", "'''"]], "[", "z", "]"]], "-", RowBox[List["24", " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], " ", RowBox[List["w", "[", "z", "]"]]]], "+", RowBox[List["36", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], "2"]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["DedekindEta", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List["DedekindEta", "[", "z", "]"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> w </mi> <mi> &#8242;&#8242;&#8242; </mi> </msup> <mo> [ </mo> <mi> z </mi> <mo> ] </mo> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mi> &#951; </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mrow> <mi> &#951; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Eta]&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[DedekindEta[Slot[1]]]]] </annotation> </semantics> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <apply> <power /> <ci> w </ci> <ci> &#8242;&#8242;&#8242; </ci> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> &#951; </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ci> DedekindEta </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]], "-", RowBox[List["24", " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], " ", RowBox[List["w", "[", "z_", "]"]]]], "+", RowBox[List["36", " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["DedekindEta", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List["DedekindEta", "[", "z", "]"]]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29