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WeierstrassZetaHalfPeriodValues




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZetaHalfPeriodValues[{g2,g3}] > Differentiation > Low-order differentiation > With respect to omega3





http://functions.wolfram.com/09.21.20.0005.01









  


  








Input Form





D[Subscript[\[Eta], 1], Subscript[\[Omega], 3]] == (-(Subscript[\[Omega], 1]/(Pi Subscript[\[Omega], 3]))) Sqrt[-(Subscript[\[Omega], 3]^2/Subscript[\[Omega], 1]^2)] (2 Subscript[\[Eta], 1]^2 - (1/6) Subscript[g, 2] Subscript[\[Omega], 1]^2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["\[Omega]", "3"]], SubscriptBox["\[Eta]", "1"]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[SubscriptBox["\[Omega]", "1"], RowBox[List["\[Pi]", " ", SubscriptBox["\[Omega]", "3"]]]]]], " ", SqrtBox[RowBox[List["-", FractionBox[SubsuperscriptBox["\[Omega]", "3", "2"], SubsuperscriptBox["\[Omega]", "1", "2"]]]]], RowBox[List["(", RowBox[List[RowBox[List["2", SubsuperscriptBox["\[Eta]", "1", "2"]]], "-", RowBox[List[FractionBox["1", "6"], SubscriptBox["g", "2"], SubsuperscriptBox["\[Omega]", "1", "2"]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <msub> <mi> &#951; </mi> <mn> 1 </mn> </msub> </mrow> <mrow> <mo> &#8706; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mfrac> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> &#969; </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> <msubsup> <mi> &#969; </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msubsup> <mi> &#951; </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msubsup> <mi> &#969; </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> D </ci> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <pi /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["\[Omega]_", "3"]]]], SubscriptBox["\[Eta]_", "1"]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], " ", SqrtBox[RowBox[List["-", FractionBox[SubsuperscriptBox["\[Omega]\[Omega]", "3", "2"], SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SubsuperscriptBox["\[Eta]\[Eta]", "1", "2"]]], "-", RowBox[List[FractionBox["1", "6"], " ", SubscriptBox["g", "2"], " ", SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]]]], ")"]]]], RowBox[List["\[Pi]", " ", SubscriptBox["\[Omega]\[Omega]", "3"]]]]]]]]]]


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





2002-12-18