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 ArcSin

 http://functions.wolfram.com/01.12.27.1286.01

 Input Form

 ArcSin[1 - 2 z^2] == (3 Pi)/2 + 2 I ArcCosh[z] /; Inequality[Pi/2, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", "\[Pi]"]], "2"], "+", RowBox[List["2", "\[ImaginaryI]", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

 sin - 1 ( 1 - 2 z 2 ) 2 cosh - 1 ( z ) + 3 π 2 /; π 2 < arg ( z ) π Condition 1 -1 2 z 2 2 z 3 2 -1 Inequality 2 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["3", " ", "\[Pi]"]], "2"], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

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

 2003-08-21