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 ArcSin

 http://functions.wolfram.com/01.12.27.1725.01

 Input Form

 ArcSin[z] == -(Pi/2) - I ArcCoth[Sqrt[z^2/(z^2 - 1)]] /; -Pi < Arg[z] < -(Pi/2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 sin - 1 ( z ) - coth - 1 ( z 2 z 2 - 1 ) - π 2 /; - π < arg ( z ) < - π 2 Condition z -1 z 2 z 2 -1 -1 1 2 -1 2 -1 -1 z -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]]]

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

 2003-08-21