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WeierstrassP




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Differentiation > Low-order differentiation > With respect to omega3





http://functions.wolfram.com/09.13.20.0013.02









  


  








Input Form





D[WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}], Subscript[\[Omega], 3]] == ((2 Subscript[\[Omega], 1])/ (Pi Subscript[\[Omega], 3])) Sqrt[-(Subscript[\[Omega], 3]^2/Subscript[\[Omega], 1]^2)] (Subscript[\[Omega], 1] (2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] - Subscript[g, 2]/3) - Subscript[\[Eta], 1] (2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] + z WeierstrassPPrime[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["\[Omega]_", "3"]]]], RowBox[List["WeierstrassP", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "1"]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SubsuperscriptBox["\[Omega]\[Omega]", "3", "2"], SubsuperscriptBox["\[Omega]\[Omega]", "1", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["WeierstrassZeta", "[", 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"]]], "}"]]]], "]"]]]], "-", FractionBox[SubscriptBox["gg", "2"], "3"]]], ")"]]]], "-", RowBox[List[SubscriptBox["\[Eta]", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List["z", " ", RowBox[List["WeierstrassPPrime", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["\[Pi]", " ", SubscriptBox["\[Omega]\[Omega]", "3"]]]]]]]]


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





2002-12-18