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variants of this functions
EllipticTheta






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[3,z,q] > Series representations > q-series > Expansions at generic point z==z0





http://functions.wolfram.com/09.03.06.0021.01









  


  










Input Form





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










Standard Form





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










MathML Form







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Rule Form





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










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





2007-05-02





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