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WeierstrassZeta




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.17.20.0005.01









  


  








Input Form





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








Standard Form





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MathML Form







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</ci> </apply> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["g_", "2"]]]], RowBox[List["WeierstrassZeta", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", SubsuperscriptBox["gg", "2", "2"]]], ")"]]]], "-", RowBox[List["z", " ", SubscriptBox["gg", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SubscriptBox["gg", "2"], " ", RowBox[List["WeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "+", RowBox[List["3", " ", SubscriptBox["gg", "3"]]]]], ")"]]]], "+", RowBox[List["18", " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassPPrime", "[", 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