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WeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Differential equations > Ordinary nonlinear differential equations





http://functions.wolfram.com/09.13.13.0002.01









  


  










Input Form





Derivative[2][w][z] - 6 w[z]^2 + Subscript[g, 2]/2 == 0 /; w[z] == WeierstrassP[z + a, {Subscript[g, 2], Subscript[g, 3]}]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[DoublePrime]"], "[", "z", "]"]], "-", RowBox[List["6", SuperscriptBox[RowBox[List["w", "[", "z", "]"]], "2"]]], "+", FractionBox[SubscriptBox["g", "2"], "2"]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List["z", "+", "a"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]










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> <msup> <mi> w </mi> <mo> &#8243; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mfrac> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mn> 2 </mn> </mfrac> </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> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> z </mi> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <ci> WeierstrassP </ci> <apply> <plus /> <ci> a </ci> <ci> z </ci> </apply> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]], "-", RowBox[List["6", " ", SuperscriptBox[RowBox[List["w", "[", "z_", "]"]], "2"]]], "+", FractionBox[SubscriptBox["g_", "2"], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List["z", "+", "a"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]]]










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





2001-10-29