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 ArcCosh

 http://functions.wolfram.com/01.26.27.0469.01

 Input Form

 ArcCosh[z] == (-Pi) I - 2 I ArcTan[Sqrt[-z - 1]/Sqrt[z - 1]] /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "\[Pi]"]], " ", "\[ImaginaryI]"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 cosh - 1 ( z ) - π - 2 tan - 1 ( - z - 1 z - 1 ) /; Im ( z ) < 0 Condition z -1 -1 2 -1 z -1 1 2 z -1 1 2 -1 z 0 [/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["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], SqrtBox[RowBox[List["z", "-", "1"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-08-21