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WeierstrassZetaHalfPeriodValues






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.21.20.0002.01









  


  










Input Form





D[WeierstrassZetaHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 3]] == (1/(4 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2))) (-6 WeierstrassZetaHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] (2 Subscript[g, 2] WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] + 3 Subscript[g, 3]) + (18 Subscript[g, 3] WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] + Subscript[g, 2]^2) WeierstrassPHalfPeriodsSet[ {Subscript[g, 2], Subscript[g, 3]}] - 6 Subscript[g, 2] WeierstrassPPrimeHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["g", "3"]], RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4", RowBox[List["(", RowBox[List[SubsuperscriptBox["g", "2", "3"], "-", RowBox[List["27", SubsuperscriptBox["g", "3", "2"]]]]], ")"]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List["2", SubscriptBox["g", "2"], " ", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "+", RowBox[List["3", SubscriptBox["g", "3"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["18", SubscriptBox["g", "3"], RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "+", SubsuperscriptBox["g", "2", "2"]]], ")"]], RowBox[List["WeierstrassPHalfPeriodsSet", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "-", RowBox[List["6", " ", SubscriptBox["g", "2"], " ", RowBox[List["WeierstrassPPrimeHalfPeriodValues", "[", 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> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> { </mo> <mrow> <mstyle scriptlevel='0'> <msub> <mi> &#951; </mi> <mn> 1 </mn> </msub> </mstyle> <mstyle scriptlevel='0'> <mo> , </mo> </mstyle> <mstyle scriptlevel='0'> <msub> <mi> &#951; </mi> <mn> 2 </mn> </msub> </mstyle> <mo> , </mo> <mstyle scriptlevel='0'> <msub> <mi> &#951; </mi> <mn> 3 </mn> </msub> </mstyle> </mrow> <mstyle scriptlevel='0'> <mo> } </mo> </mstyle> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mo> - </mo> <mrow> <mn> 27 </mn> <mo> &#8290; </mo> <msubsup> <mi> g </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> + </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> e </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <msubsup> <mi> e </mi> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> , </mo> <msubsup> <mi> e </mi> <mn> 2 </mn> <mo> &#8242; </mo> </msubsup> <mo> , </mo> <msubsup> <mi> e </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mrow> <mo> } </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> e </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <mstyle scriptlevel='0'> <msub> <mi> &#951; </mi> <mn> 1 </mn> </msub> </mstyle> <mstyle scriptlevel='0'> <mo> , </mo> </mstyle> <mstyle scriptlevel='0'> <msub> <mi> &#951; </mi> <mn> 2 </mn> </msub> </mstyle> <mo> , </mo> <mstyle scriptlevel='0'> <msub> <mi> &#951; </mi> <mn> 3 </mn> </msub> </mstyle> </mrow> <mstyle scriptlevel='0'> <mo> } </mo> </mstyle> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> D </ci> <list> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 3 </cn> </apply> </list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <list> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> <list> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <list> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <list> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> <list> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#951; </ci> <cn type='integer'> 3 </cn> </apply> </list> </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["g_", "3"]]]], RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SubscriptBox["gg", "2"], " ", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "+", RowBox[List["3", " ", SubscriptBox["gg", "3"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "+", SubsuperscriptBox["gg", "2", "2"]]], ")"]], " ", RowBox[List["WeierstrassPHalfPeriodsSet", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "-", RowBox[List["6", " ", SubscriptBox["gg", "2"], " ", RowBox[List["WeierstrassPPrimeHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["gg", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["gg", "3", "2"]]]]], ")"]]]]]]]]]










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





2001-10-29





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