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 ArcSinh

 http://functions.wolfram.com/01.25.04.0012.01

 Input Form

 Limit[(ArcSin h)[x + \[Epsilon]], \[Epsilon] -> Plus[0]] == ArcSinh[x] /; I x < -1

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29