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variants of this functions
EllipticTheta






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Differentiation > Low-order differentiation > With respect to q





http://functions.wolfram.com/09.01.20.0009.01









  


  










Input Form





D[EllipticTheta[1, z, q], q] == (-(1/(4 q))) (EllipticThetaPrime[1, z, q]^2/EllipticTheta[1, z, q]) + (1/(4 q)) EllipticTheta[3, 0, q]^2 EllipticTheta[4, 0, q]^2 (EllipticTheta[2, z, q]^2/EllipticTheta[1, z, q]) + (1/(q Pi^2)) EllipticTheta[1, z, q] (WeierstrassZeta[1, WeierstrassInvariants[{1, Log[q]/(Pi I)}]] + (Pi^2/12) (EllipticTheta[3, 0, q]^4 + EllipticTheta[4, 0, q]^4))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "q"], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["4", " ", "q", " "]]]]], FractionBox[SuperscriptBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "2"], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]], "+", RowBox[List[FractionBox["1", RowBox[List["4", " ", "q", " "]]], SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "2"], SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "2"], FractionBox[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]], "2"], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]], "+", RowBox[List[FractionBox["1", RowBox[List["q", " ", SuperscriptBox["\[Pi]", "2"]]]], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["1", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["Log", "[", "q", "]"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], "}"]], "]"]]]], "]"]], "+", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "12"], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "4"], "+", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "4"]]], ")"]]]]]], ")"]]]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["q_"]]], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z_", ",", "q_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "2"], RowBox[List[RowBox[List["(", RowBox[List["4", " ", "q"]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]], "2"]]], RowBox[List[RowBox[List["(", RowBox[List["4", " ", "q"]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["1", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["Log", "[", "q", "]"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], "}"]], "]"]]]], "]"]], "+", RowBox[List[FractionBox["1", "12"], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "4"], "+", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "4"]]], ")"]]]]]], ")"]]]], RowBox[List["q", " ", SuperscriptBox["\[Pi]", "2"]]]]]]]]]]










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





2007-05-02





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