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 ArcCosh

 http://functions.wolfram.com/01.26.27.0436.01

 Input Form

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

 Standard Form

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

 MathML Form

 cosh - 1 ( z ) π 2 - tan - 1 ( z 2 1 - z 2 ) /; 0 arg ( z ) π 2 Condition z 2 -1 -1 z 2 1 -1 z 2 -1 1 2 0 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]]]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-08-21