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 ArcSin

 http://functions.wolfram.com/01.12.27.1337.01

 Input Form

 ArcSin[Sqrt[1 - z]/Sqrt[-2 z]] == (-(1/2)) I ArcCosh[1/z] /; Im[z] <= 0

 Standard Form

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

 MathML Form

 sin - 1 ( 1 - z - 2 z ) - 1 2 cosh - 1 ( 1 z ) /; Im ( z ) 0 Condition 1 -1 z 1 2 -2 z 1 2 -1 -1 1 2 1 z -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSin", "[", FractionBox[SqrtBox[RowBox[List["1", "-", "z_"]]], SqrtBox[RowBox[List[RowBox[List["-", "2"]], " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", RowBox[List["ArcCosh", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21

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