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 ArcSin

 http://functions.wolfram.com/01.12.27.1215.01

 Input Form

 ArcSin[(z Sqrt[1 - Sqrt[1 + z^2]])/(Sqrt[2] Sqrt[z^2])] == (Sqrt[-z^4] ArcSinh[z])/(2 z^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSin", "[", FractionBox[RowBox[List["z", " ", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]]]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "4"]]]], " ", RowBox[List["ArcSinh", "[", "z", "]"]]]], RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]]]]

 MathML Form

 sin - 1 ( z 1 - z 2 + 1 2 z 2 ) - z 4 2 z 2 sinh - 1 ( z ) z 1 -1 z 2 1 1 2 1 2 2 1 2 z 2 1 2 -1 -1 z 4 1 2 2 z 2 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[RowBox[List["z_", " ", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]]]]]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[SuperscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "4"]]]], " ", RowBox[List["ArcSinh", "[", "z", "]"]]]], RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]]]]

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

 2003-08-21