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 ArcCosh

 http://functions.wolfram.com/01.26.06.0029.02

 Input Form

 ArcCosh[z] \[Proportional] I (Pi - Sqrt[2] Sqrt[z + 1] (1 + O[z + 1])) /; Im[z] >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Proportional]", RowBox[List["\[ImaginaryI]", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["z", "+", "1"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", "1"]], "]"]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]

 MathML Form

 cosh - 1 ( z ) ( π - 2 z + 1 ( 1 + O ( z + 1 ) ) ) /; Im ( z ) 0 Condition Proportional z -1 2 1 2 z 1 1 2 1 O z 1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["z", "+", "1"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", "1"]], "]"]]]], ")"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]

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

 2001-10-29