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 ArcCosh

 http://functions.wolfram.com/01.26.04.0009.01

 Input Form

 Limit[ArcCosh[x + I \[Epsilon]], \[Epsilon] -> Plus[0]] == ArcCosh[x] /; 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["ArcCosh", "[", "x", "]"]]]], "/;", RowBox[List[RowBox[List["x", "<", "1"]], "\[And]", RowBox[List["x", "\[NotEqual]", RowBox[List["-", "1"]]]]]]]]]]

 MathML Form

 lim ϵ "\[Rule]" + 0 cosh - 1 ( x + ϵ ) cosh - 1 ( x ) /; x < 1 x - 1 Condition ϵ ϵ 0 x ϵ x 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["ArcCosh", "[", "x", "]"]], "/;", RowBox[List[RowBox[List["x", "<", "1"]], "&&", RowBox[List["x", "\[NotEqual]", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2001-10-29