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 ArcCosh

 http://functions.wolfram.com/01.26.27.0399.01

 Input Form

 ArcCosh[z] == (-Pi) I - I ArcTan[Sqrt[1 - z^2]/z] /; -Pi < Arg[z] < -(Pi/2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "\[ImaginaryI]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "z"], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 cosh - 1 ( z ) - π - tan - 1 ( 1 - z 2 z ) /; - π < arg ( z ) < - π 2 Condition z -1 -1 1 -1 z 2 1 2 z -1 -1 z -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "\[ImaginaryI]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]]]

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

 2003-08-21