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 ArcSinh

 http://functions.wolfram.com/01.25.04.0011.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29