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 ArcCosh

 http://functions.wolfram.com/01.26.06.0062.01

 Input Form

 ArcCosh[z] \[Proportional] ((Pi I)/2) (2 UnitStep[Im[z]] - 1) (1 + O[z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", RowBox[List["UnitStep", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "-", "1"]], ")"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", "z", "]"]]]], ")"]]]]]]]]

 MathML Form

 cosh - 1 ( z ) π 2 ( 2 θ UnitStep ( Im ( z ) ) - 1 ) ( 1 + O ( z ) ) Proportional z 2 -1 2 UnitStep z -1 1 O z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["UnitStep", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", "z", "]"]]]], ")"]]]]]]]]

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

 2007-05-02