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 ArcCosh

 http://functions.wolfram.com/01.26.27.1275.01

 Input Form

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

 Standard Form

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

 MathML Form

 cosh - 1 ( z ) - ( π 2 - sec - 1 ( 1 1 - z 2 ) ) /; - π 2 < arg ( z ) < 0 Condition z -1 2 -1 -1 1 1 -1 z 2 -1 1 2 -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["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcSec", "[", SqrtBox[FractionBox["1", RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], "]"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-08-21