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WeierstrassPHalfPeriodValues






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.20.20.0001.01









  


  










Input Form





D[WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 2]] == (1/(4 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2))) (WeierstrassPPrimeHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] (Subscript[g, 2]^2 WeierstrassPHalfPeriodsSet[{Subscript[g, 2], Subscript[g, 3]}] - 18 Subscript[g, 3] WeierstrassZetaHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}]) - 36 Subscript[g, 3] WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}]^2 + 2 Subscript[g, 2]^2 WeierstrassPHalfPeriodValues[ {Subscript[g, 2], Subscript[g, 3]}] + 6 Subscript[g, 2] Subscript[g, 3])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["g", "2"]], RowBox[List["WeierstrassPHalfPeriodValues", "[", 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["WeierstrassPPrimeHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[SubsuperscriptBox["g", "2", "2"], RowBox[List["WeierstrassPHalfPeriodsSet", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "-", RowBox[List["18", SubscriptBox["g", "3"], " ", RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]]]], ")"]]]], "-", RowBox[List["36", SubscriptBox["g", "3"], " ", SuperscriptBox[RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]], "2"]]], "+", RowBox[List["2", SubsuperscriptBox["g", "2", "2"], " ", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "+", RowBox[List["6", SubscriptBox["g", "2"], " ", SubscriptBox["g", "3"]]]]], ")"]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["g_", "2"]]]], RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["WeierstrassPPrimeHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SubsuperscriptBox["gg", "2", "2"], " ", RowBox[List["WeierstrassPHalfPeriodsSet", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "-", RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassZetaHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]]]], ")"]]]], "-", RowBox[List["36", " ", SubscriptBox["gg", "3"], " ", SuperscriptBox[RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]], "2"]]], "+", RowBox[List["2", " ", SubsuperscriptBox["gg", "2", "2"], " ", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "+", RowBox[List["6", " ", 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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