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WeierstrassPPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.14.20.0004.01









  


  










Input Form





D[WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 2]] == (1/(8 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2))) ((-z) Subscript[g, 2]^3 + 12 z Subscript[g, 2]^2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + 6 (Subscript[g, 2]^2 - 18 Subscript[g, 3] WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]) WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + 18 Subscript[g, 3] (Subscript[g, 2] - 12 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^ 2) WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}])










Standard Form





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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["WeierstrassPPrime", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "z"]], " ", SubsuperscriptBox["gg", "2", "3"]]], "+", RowBox[List["12", " ", "z", " ", SubsuperscriptBox["gg", "2", "2"], " ", SuperscriptBox[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List[SubsuperscriptBox["gg", "2", "2"], "-", RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], ")"]], " ", RowBox[List["WeierstrassPPrime", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["(", RowBox[List[SubscriptBox["gg", "2"], "-", RowBox[List["12", " ", SuperscriptBox[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"]]]]], ")"]], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], RowBox[List["8", " ", 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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