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 ArcSin

 http://functions.wolfram.com/01.12.27.1024.01

 Input Form

 ArcSin[Sqrt[(1 - Sqrt[1 + z^2])/2]] == (1/2) ArcCsc[I/z] /; Inequality[0, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]], "2"]], " ", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], RowBox[List["ArcCsc", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

 sin - 1 ( 1 2 ( 1 - z 2 + 1 ) ) 1 2 csc - 1 ( z ) /; 0 < arg ( z ) π Condition 1 2 1 -1 z 2 1 1 2 1 2 1 2 z -1 Inequality 0 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", SqrtBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]]]], ")"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCsc", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

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

 2003-08-21