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 EllipticF

 http://functions.wolfram.com/08.05.21.0004.01

 Input Form

 Integrate[EllipticF[z, m]/Sqrt[1 - m Sin[z]^2], z] == (1/2) EllipticF[z, m]^2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]], SqrtBox[RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]]]]]]

 MathML Form

 F ( z m ) 1 - m sin 2 ( z ) z 1 2 F ( z m ) 2 z EllipticF z m 1 -1 m z 2 1 2 -1 1 2 EllipticF z m 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["EllipticF", "[", RowBox[List["z_", ",", "m_"]], "]"]], SqrtBox[RowBox[List["1", "-", RowBox[List["m_", " ", SuperscriptBox[RowBox[List["Sin", "[", "z_", "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]]]]]]

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

 2001-10-29