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WeierstrassP




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.13.20.0005.01









  


  








Input Form





D[WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 2]] == (1/(4 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2))) (WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] (Subscript[g, 2]^2 z - 18 Subscript[g, 3] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) - 36 Subscript[g, 3] WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + 2 Subscript[g, 2]^2 WeierstrassP[z, {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["WeierstrassP", "[", RowBox[List["z", ",", 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["WeierstrassPPrime", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[SubsuperscriptBox["g", "2", "2"], " ", "z"]], "-", RowBox[List["18", SubscriptBox["g", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]], ")"]]]], "-", RowBox[List["36", SubscriptBox["g", "3"], " ", SuperscriptBox[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List["2", SubsuperscriptBox["g", "2", "2"], " ", RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", 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["WeierstrassP", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SubsuperscriptBox["gg", "2", "2"], " ", "z"]], "-", RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], ")"]]]], "-", RowBox[List["36", " ", SubscriptBox["gg", "3"], " ", SuperscriptBox[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List["2", " ", SubsuperscriptBox["gg", "2", "2"], " ", RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", 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