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 ArcSin

 http://functions.wolfram.com/01.12.04.0013.01

 Input Form

 Limit[ArcSin[x + I \[Epsilon]], \[Epsilon] -> Plus[0]] == -ArcSin[x] + Pi /; x > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]"]]]], "]"]], ",", RowBox[List["\[Epsilon]", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "\[Equal]", " ", RowBox[List[RowBox[List["-", RowBox[List["ArcSin", "[", "x", "]"]]]], "+", "\[Pi]"]]]], "/;", RowBox[List["x", ">", "1"]]]]]]

 MathML Form

 lim ϵ "\[Rule]" + 0 sin - 1 ( x + ϵ ) π - sin - 1 ( x ) /; x > 1 Condition ϵ ϵ 0 x ϵ -1 x x 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["ArcSin", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "\[Epsilon]_"]]]], "]"]], ",", RowBox[List["\[Epsilon]_", "\[Rule]", RowBox[List["+", "0"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["ArcSin", "[", "x", "]"]]]], "+", "\[Pi]"]], "/;", RowBox[List["x", ">", "1"]]]]]]]]

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

 2001-10-29