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 EllipticE

 http://functions.wolfram.com/08.01.07.0001.01

 Input Form

 EllipticE[z] == Integrate[Sqrt[1 - z Sin[t]^2], {t, 0, Pi/2}] /; Abs[Arg[1 - z]] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticE", "[", "z", "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[SqrtBox[RowBox[List["1", "-", RowBox[List["z", " ", SuperscriptBox[RowBox[List["Sin", "[", "t", "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "/;", " ", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["1", "-", "z"]], "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 E ( z ) 0 π 2 1 - z sin 2 ( t ) t /; "\[LeftBracketingBar]" arg ( 1 - z ) "\[RightBracketingBar]" < π Condition EllipticE z t 0 2 -1 1 -1 z t 2 1 2 1 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticE", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[List[SqrtBox[RowBox[List["1", "-", RowBox[List["z", " ", SuperscriptBox[RowBox[List["Sin", "[", "t", "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["1", "-", "z"]], "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2001-10-29