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 ArcSin

 http://functions.wolfram.com/01.12.27.1041.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21