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variants of this functions
EllipticThetaPrime






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[2,z,q] > Series representations > q-series > Expansions at q==1





http://functions.wolfram.com/09.06.06.0015.01









  


  










Input Form





EllipticThetaPrime[2, z, q] \[Proportional] (((2 Sqrt[Pi] I)/(q - 1)^(3/2)) (1 + O[q - 1]) E^(z^2/Log[q]) (z - 2 E^(Pi^2/Log[q]) (z Cosh[(2 Pi z)/Log[q]] + Pi Sinh[(2 Pi z)/Log[q]]) + O[E^((4 Pi^2)/Log[q]) (z Cosh[(4 Pi z)/Log[q]] + 2 Pi Sinh[(4 Pi z)/Log[q]])]))/ E^(3 I Pi Floor[3/4 - Arg[q - 1]/(2 Pi)]) /; Abs[q] < 1










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticThetaPrime", "[", RowBox[List["2", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "3"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["3", "4"], "-", FractionBox[RowBox[List["Arg", "[", RowBox[List["q", "-", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["q", "-", "1"]], "]"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["z", "2"], RowBox[List["Log", "[", "q", "]"]]]], " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["\[Pi]", "2"], RowBox[List["Log", "[", "q", "]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "z"]], RowBox[List["Log", "[", "q", "]"]]], "]"]]]], "+", RowBox[List["\[Pi]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "z"]], RowBox[List["Log", "[", "q", "]"]]], "]"]]]]]], ")"]]]], "+", RowBox[List["O", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["4", " ", SuperscriptBox["\[Pi]", "2"]]], RowBox[List["Log", "[", "q", "]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["4", " ", "\[Pi]", " ", "z"]], RowBox[List["Log", "[", "q", "]"]]], "]"]]]], "+", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["4", " ", "\[Pi]", " ", "z"]], RowBox[List["Log", "[", "q", "]"]]], "]"]]]]]], ")"]]]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", "1"]], ")"]], RowBox[List["3", "/", "2"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "q", "]"]], "<", "1"]]]]]]]]










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





2007-05-02