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 ArcSin

 http://functions.wolfram.com/01.12.27.1547.01

 Input Form

 ArcSin[(z + 1)/(z - 1)] == -2 I ArcTanh[Sqrt[z]] + (3 Pi)/2 /; Element[z, Reals] && z > 1

 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[RowBox[List["-", "2"]], "\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]], "+", FractionBox[RowBox[List["3", "\[Pi]"]], "2"]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", ">", "1"]]]], ")"]]]]]]

 MathML Form

 sin - 1 ( z + 1 z - 1 ) - 2 tanh - 1 ( z ) + 3 π 2 /; ( z z > 1 ) Condition z 1 z -1 -1 -2 z 1 2 3 2 -1 z z 1 [/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[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]], "+", FractionBox[RowBox[List["3", " ", "\[Pi]"]], "2"]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", ">", "1"]]]]]]]]]]

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

 2003-08-21