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 ArcSin

 http://functions.wolfram.com/01.12.27.1203.01

 Input Form

 ArcSin[Sqrt[-1 - z^2]/Sqrt[-z^2]] == Pi/2 - I ArcSinh[1/z] /; Inequality[0, LessEqual, Arg[z], Less, Pi]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21