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 ArcSin

 http://functions.wolfram.com/01.12.27.0503.01

 Input Form

 ArcSin[(z - 1)/(z + 1)] == -2 ArcTan[1/Sqrt[z]] + Pi/2 /; Abs[Arg[z]] < Pi

 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"]], RowBox[List["ArcTan", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "+", FractionBox["\[Pi]", "2"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 sin - 1 ( z - 1 z + 1 ) - 2 tan - 1 ( 1 z ) + π 2 /; ​​ "\[LeftBracketingBar]" arg ( z ) "\[RightBracketingBar]" < π Condition z -1 z 1 -1 -2 1 z 1 2 -1 2 -1 z [/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"]], " ", RowBox[List["ArcTan", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "+", FractionBox["\[Pi]", "2"]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21