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 ArcSin

 http://functions.wolfram.com/01.12.27.1139.01

 Input Form

 ArcSin[z] == -(Pi/2) - 2 (Sqrt[-z - 1]/Sqrt[1 + z]) ArcSinh[Sqrt[(-z - 1)/2]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "-", RowBox[List["2", " ", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], SqrtBox[RowBox[List["1", "+", "z"]]]], " ", RowBox[List["ArcSinh", "[", SqrtBox[FractionBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]], "2"]], "]"]]]]]]]]]]

 MathML Form

 sin - 1 ( z ) - 2 - z - 1 z + 1 sinh - 1 ( 1 2 ( - z - 1 ) ) - π 2 z -1 2 -1 z -1 1 2 z 1 1 2 -1 1 2 -1 z -1 1 2 -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "-", FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], " ", RowBox[List["ArcSinh", "[", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "z"]], "-", "1"]], ")"]]]]], "]"]]]], SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]]

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

 2003-08-21