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 ArcSin

 http://functions.wolfram.com/01.12.27.1218.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21