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variants of this functions
EllipticTheta






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Identities involving the group of functions > Differential identities





http://functions.wolfram.com/09.01.18.0168.01









  


  










Input Form





Derivative[0, 4, 0][EllipticTheta][2, 0, q]/EllipticTheta[2, 0, q] - 3 (Derivative[0, 2, 0][EllipticTheta][2, 0, q]^2/ EllipticTheta[2, 0, q]^2) == (-((32 Subscript[\[Omega], 1]^4)/Pi^4)) (Subscript[e, 1] - Subscript[e, 2]) (Subscript[e, 1] - Subscript[e, 3]) /; {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Omega], 2] == -Subscript[\[Omega], 1] - Subscript[\[Omega], 3] && q == Exp[Pi I (Subscript[\[Omega], 3]/Subscript[\[Omega], 1])] && Subscript[e, n] == WeierstrassP[Subscript[\[Omega], n], {Subscript[g, 2], Subscript[g, 3]}] && Element[n, {1, 2, 3}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "4", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["2", ",", "0", ",", "q_"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q_"]], "]"]]], "-", FractionBox[RowBox[List["3", " ", SuperscriptBox[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "2", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["2", ",", "0", ",", "q_"]], "]"]], "2"]]], SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q_"]], "]"]], "2"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["32", " ", SubsuperscriptBox["\[Omega]", "1", "4"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["e", "1"], "-", SubscriptBox["e", "3"]]], ")"]]]], SuperscriptBox["\[Pi]", "4"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "&&", RowBox[List[SubscriptBox["\[Omega]", "2"], "\[Equal]", RowBox[List[RowBox[List["-", SubscriptBox["\[Omega]", "1"]]], "-", SubscriptBox["\[Omega]", "3"]]]]], "&&", RowBox[List["q", "\[Equal]", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", SubscriptBox["\[Omega]", "3"]]], SubscriptBox["\[Omega]", "1"]]]]], "&&", RowBox[List[SubscriptBox["e", "n"], "\[Equal]", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "n"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "&&", RowBox[List["n", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]]]]










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





2001-10-29





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