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 ArcSin

 http://functions.wolfram.com/01.12.27.1525.01

 Input Form

 ArcSin[(z - 1)/(z + 1)] == 2 I ArcTanh[1/Sqrt[-z]] + Pi/2 /; Im[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["2", "\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]], "+", FractionBox["\[Pi]", "2"]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 sin - 1 ( z - 1 z + 1 ) 2 tanh - 1 ( 1 - z ) + π 2 /; Im ( z ) > 0 Condition z -1 z 1 -1 2 1 -1 z 1 2 -1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[RowBox[List["z_", "-", "1"]], RowBox[List["z_", "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]], "+", FractionBox["\[Pi]", "2"]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2003-08-21