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 ArcSin

 http://functions.wolfram.com/01.12.27.1396.01

 Input Form

 ArcSin[2 z Sqrt[1 - z^2]] == Pi + 2 I ArcCosh[z] /; Pi/4 <= Arg[z] <= (3 Pi)/4

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["2", " ", "z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], "]"]], "\[Equal]", RowBox[List["\[Pi]", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "4"], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["3", "\[Pi]"]], "4"]]]]]]]

 MathML Form

 sin - 1 ( 2 z 1 - z 2 ) π + 2 cosh - 1 ( z ) /; π 4 arg ( z ) 3 π 4 Condition 2 z 1 -1 z 2 1 2 2 z 4 -1 z 3 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", RowBox[List["2", " ", "z_", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "4"], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["3", " ", "\[Pi]"]], "4"]]]]]]]]]

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

 2003-08-21