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variants of this functions
EllipticE




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z,m] > Series representations > Generalized power series > Expansions at generic point m==m0 > For the function itself





http://functions.wolfram.com/08.04.06.0048.01









  


  








Input Form





EllipticE[z, m] \[Proportional] EllipticE[z, Subscript[m, 0]] + ((EllipticE[z, Subscript[m, 0]] - EllipticF[z, Subscript[m, 0]])/ (2 Subscript[m, 0])) (m - Subscript[m, 0]) + (1/(16 (-1 + Subscript[m, 0]) Subscript[m, 0]^2 Sqrt[1 - Subscript[m, 0] Sin[z]^2])) (2 Sqrt[1 - Subscript[m, 0] Sin[z]^2] ((-(-2 + Subscript[m, 0])) EllipticE[z, Subscript[m, 0]] + 2 (-1 + Subscript[m, 0]) EllipticF[z, Subscript[m, 0]]) - Subscript[m, 0] Sin[2 z]) (m - Subscript[m, 0])^2 + O[(m - Subscript[m, 0])^3]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticE", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List["z", ",", SubscriptBox["mm", "0"]]], "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List["z", ",", SubscriptBox["mm", "0"]]], "]"]], "-", RowBox[List["EllipticF", "[", RowBox[List["z", ",", SubscriptBox["mm", "0"]]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["m", "-", SubscriptBox["mm", "0"]]], ")"]]]], RowBox[List["2", " ", SubscriptBox["mm", "0"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", RowBox[List[SubscriptBox["mm", "0"], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", SubscriptBox["mm", "0"]]], ")"]]]], " ", RowBox[List["EllipticE", "[", RowBox[List["z", ",", SubscriptBox["mm", "0"]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["mm", "0"]]], ")"]], " ", RowBox[List["EllipticF", "[", RowBox[List["z", ",", SubscriptBox["mm", "0"]]], "]"]]]]]], ")"]]]], "-", RowBox[List[SubscriptBox["mm", "0"], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", SubscriptBox["mm", "0"]]], ")"]], "2"]]], RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["mm", "0"]]], ")"]], " ", SubsuperscriptBox["mm", "0", "2"], " ", SqrtBox[RowBox[List["1", "-", RowBox[List[SubscriptBox["mm", "0"], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]]]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["m", "-", SubscriptBox["mm", "0"]]], "]"]], "3"]]]]]]]


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





2007-05-02