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variants of this functions
EllipticE






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z] > Complex characteristics > Real part





http://functions.wolfram.com/08.01.19.0001.01









  


  










Input Form





Re[EllipticE[x + I y]] == (Pi/2) HypergeometricPFQ[{{3/4, 5/4, 1/4, 3/4}, {}, {}}, {{1, 3/2}, {1/2}, {3/2}}, -y^2, x^2] - ((Pi x)/8) HypergeometricPFQ[{{1/4, 3/4, -(1/4), 1/4}, {}, {}}, {{1, 1/2}, {1/2}, {1/2}}, -y^2, x^2] /; Element[x, Reals] && Element[y, Reals]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Re", "[", RowBox[List["EllipticE", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["1", "4"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]]]], "}"]], ",", RowBox[List["-", SuperscriptBox["y", "2"]]], ",", SuperscriptBox["x", "2"]]], "]"]]]], "-", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "x"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["3", "4"], ",", RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["-", SuperscriptBox["y", "2"]]], ",", SuperscriptBox["x", "2"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]










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





2001-10-29





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