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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[z,{g2,g3}] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.15.13.0004.01









  


  








Input Form





(Subscript[g, 2]^3 - 27 Subscript[g, 3]^2) D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 2]] == (-(9/4)) Subscript[g, 3] D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], {z, 2}] - (1/4) Subscript[g, 2]^2 WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}] - (3/16) Subscript[g, 2] Subscript[g, 3] z^2 WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}] + (1/4) Subscript[g, 2]^2 z D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["(", RowBox[List[SubsuperscriptBox["g_", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["g_", "3", "2"]]]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["g_", "2"]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["-", "9"]], ")"]], " ", SubscriptBox["gg", "3"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], "-", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["gg", "2", "2"], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "-", RowBox[List[FractionBox["3", "16"], " ", SubscriptBox["gg", "2"], " ", SubscriptBox["gg", "3"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["gg", "2", "2"], " ", "z", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]]]]]]]]


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





2001-10-29