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 ArcSin

 http://functions.wolfram.com/01.12.27.0184.02

 Input Form

 ArcSin[Sqrt[(1 - z)/2]] == (-(I/2)) ArcCosh[z] /; Inequality[0, Less, Arg[z], LessEqual, Pi] || 0 < z < 1

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29