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WeierstrassHalfPeriods




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.18.20.0007.01









  


  








Input Form





D[WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 3]] == (1/(2 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2))) (-6 Subscript[g, 2] WeierstrassZeta[WeierstrassHalfPeriods[ {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], Subscript[g, 3]}] + 9 Subscript[g, 3] WeierstrassHalfPeriods[ {Subscript[g, 2], Subscript[g, 3]}])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["g", "3"]], RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["g", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["g", "3", "2"]]]]], ")"]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", SubscriptBox["g", "2"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List["9", " ", SubscriptBox["g", "3"], " ", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[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_", "3"]]]], RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", SubscriptBox["gg", "2"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List["9", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["gg", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["gg", "3", "2"]]]]], ")"]]]]]]]]]


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





2007-05-02