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 ArcCosh

 http://functions.wolfram.com/01.26.27.1374.01

 Input Form

 ArcCosh[Sqrt[(z^2 - 1)/z^2]] == I (Pi/2 - ArcSec[z]) /; Inequality[0, LessEqual, Arg[z], Less, Pi]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21