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 ArcSin

 http://functions.wolfram.com/01.12.27.0176.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29