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variants of this functions
EllipticE




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z,m] > Representations through more general functions > Through Meijer G > Classical cases involving tan-1 in the arguments





http://functions.wolfram.com/08.04.26.0003.01









  


  








Input Form





EllipticE[ArcTan[z^(1/4)], 1 - 1/z] == (-(1/(4 Pi))) MeijerG[{{0, 1}, {}}, {{-(1/2), 1/2}, {}}, z] + (Sqrt[z] - 1)/(2 Sqrt[z]) /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["ArcTan", "[", SuperscriptBox["z", FractionBox["1", "4"]], "]"]], ",", RowBox[List["1", "-", FractionBox["1", "z"]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["4", "\[Pi]"]]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], "+", FractionBox[RowBox[List[SqrtBox["z"], "-", "1"]], RowBox[List["2", SqrtBox["z"]]]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["ArcTan", "[", SuperscriptBox["z_", RowBox[List["1", "/", "4"]]], "]"]], ",", RowBox[List["1", "-", FractionBox["1", "z_"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]], RowBox[List["4", " ", "\[Pi]"]]]]], "+", FractionBox[RowBox[List[SqrtBox["z"], "-", "1"]], RowBox[List["2", " ", SqrtBox["z"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29