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 ArcCosh

 http://functions.wolfram.com/01.26.04.0011.01

 Input Form

 Limit[ArcCosh[x - I \[Epsilon]], \[Epsilon] -> Plus[0]] == -ArcCosh[x] /; -1 < x < 1

 Standard Form

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

 MathML Form

 lim ϵ "\[Rule]" + 0 cosh - 1 ( x - ϵ ) - cosh - 1 ( x ) /; - 1 < x < 1 Condition ϵ ϵ 0 x -1 ϵ -1 x -1 x 1 [/itex]

 Rule Form

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

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

 2001-10-29