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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[1,z,q] > Series representations > q-series > Expansions at generic point q==q0





http://functions.wolfram.com/09.05.06.0007.01









  


  








Input Form





EllipticThetaPrime[1, z, q] \[Proportional] EllipticThetaPrime[1, z, Subscript[q, 0]] + Derivative[0, 1, 1][EllipticTheta][1, z, Subscript[q, 0]] (q - Subscript[q, 0]) + (1/2) Derivative[0, 1, 2][EllipticTheta][1, z, Subscript[q, 0]] (q - Subscript[q, 0])^2 + (1/6) Derivative[0, 1, 3][EllipticTheta][1, z, Subscript[q, 0]] (q - Subscript[q, 0])^3 + O[(q - Subscript[q, 0])^4]








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["1", ",", "z_", ",", "q_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], "+", RowBox[List[RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "1"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]], "2"]]], "+", RowBox[List[FractionBox["1", "6"], " ", RowBox[List[SuperscriptBox["EllipticTheta", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "3"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["1", ",", "z", ",", SubscriptBox["qq", "0"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], ")"]], "3"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["q", "-", SubscriptBox["qq", "0"]]], "]"]], "4"]]]]]]]


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





2007-05-02