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WeierstrassHalfPeriods






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.18.20.0006.01









  


  










Input Form





D[WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], 2}] == (1/(16 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2)^2)) (5 Subscript[g, 2]^4 WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] + 189 Subscript[g, 2] Subscript[g, 3]^2 WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] + 162 Subscript[g, 3]^2 WeierstrassPPrime[WeierstrassHalfPeriods[ {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], Subscript[g, 3]}] - 216 Subscript[g, 2]^2 Subscript[g, 3] WeierstrassZeta[WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], Subscript[g, 3]}])










Standard Form





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MathML Form







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</ms> <ci> WeierstrassPPrime </ci> </apply> <ms> &#8242; </ms> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> { </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> &#969; </ms> <ms> 1 </ms> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> &#969; </ms> <ms> 3 </ms> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> } </ms> </list> </apply> <ms> ; </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> g </ms> <ms> 3 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", "2"]], "}"]]]]], RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["5", " ", SubsuperscriptBox["gg", "2", "4"], " ", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "+", RowBox[List["189", " ", SubscriptBox["gg", "2"], " ", SubsuperscriptBox["gg", "3", "2"], " ", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "+", RowBox[List["162", " ", SubsuperscriptBox["gg", "3", "2"], " ", RowBox[List["WeierstrassPPrime", "[", RowBox[List[RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "-", RowBox[List["216", " ", SubsuperscriptBox["gg", "2", "2"], " ", SubscriptBox["gg", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], RowBox[List["16", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubsuperscriptBox["gg", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["gg", "3", "2"]]]]], ")"]], "2"]]]]]]]]










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





2007-05-02