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 ArcSin

 http://functions.wolfram.com/01.12.16.0098.01

 Input Form

 ArcSin[Sqrt[(z - Sqrt[z^2 - 1])/(2 z)]] == (1/2) ArcSin[1/z] + Pi/2 /; Re[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z", "-", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], RowBox[List["2", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["ArcSin", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox["\[Pi]", "2"]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 sin - 1 ( z - z 2 - 1 2 z ) 1 2 sin - 1 ( 1 z ) + π 2 /; Re ( z ) < 0 Condition z -1 z 2 -1 1 2 2 z -1 1 2 1 2 1 z -1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]]], RowBox[List["2", " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSin", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox["\[Pi]", "2"]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-08-21