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 ArcSin

 http://functions.wolfram.com/01.12.27.1133.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox[SuperscriptBox["z", "2"]], RowBox[List["2", "z"]]], RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List["\[ImaginaryI]", RowBox[List["(", RowBox[List[RowBox[List["2", SuperscriptBox["z", "2"]]], "-", "1"]], ")"]]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-08-21