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 ArcSin

 http://functions.wolfram.com/01.12.27.1084.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21