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 EllipticF

 http://functions.wolfram.com/08.05.03.0009.01

 Input Form

 EllipticF[(-I) Infinity, m] == (1/Sqrt[m]) EllipticK[1/m] - EllipticK[m] /; 0 < m < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticF", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Infinity]"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", SqrtBox["m"]], RowBox[List["EllipticK", "[", FractionBox["1", "m"], "]"]]]], "-", RowBox[List["EllipticK", "[", "m", "]"]]]]]], "/;", RowBox[List["0", "<", "m", "<", "1"]]]]]]

 MathML Form

 F ( - m ) 1 m K ( 1 m ) - K ( m ) /; 0 < m < 1 Condition EllipticF -1 m 1 m 1 2 -1 EllipticK 1 m -1 -1 EllipticK m 0 m 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Infinity]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["EllipticK", "[", FractionBox["1", "m"], "]"]], SqrtBox["m"]], "-", RowBox[List["EllipticK", "[", "m", "]"]]]], "/;", RowBox[List["0", "<", "m", "<", "1"]]]]]]]]

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

 2001-10-29