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 InverseJacobiND

 http://functions.wolfram.com/09.44.03.0014.01

 Input Form

 InverseJacobiND[-Infinity, m] == (1/Sqrt[m - 1]) EllipticK[1/(1 - m)] + 2 I EllipticK[1 - m]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["InverseJacobiND", "[", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", SqrtBox[RowBox[List["m", "-", "1"]]]], RowBox[List["EllipticK", "[", FractionBox["1", RowBox[List["1", "-", "m"]]], "]"]]]], "+", RowBox[List["2", "\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]]]]]]]]]]

 MathML Form

 nd - 1 ( - m ) 1 m - 1 K ( 1 1 - m ) + 2 K ( 1 - m ) InverseJacobiND -1 m 1 m -1 1 2 -1 EllipticK 1 1 -1 m -1 2 EllipticK 1 -1 m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiND", "[", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["EllipticK", "[", FractionBox["1", RowBox[List["1", "-", "m"]]], "]"]], SqrtBox[RowBox[List["m", "-", "1"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]]]]]]]]]]

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

 2001-10-29