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 ArcCosh

 http://functions.wolfram.com/01.26.27.0317.01

 Input Form

 ArcCosh[Sqrt[(z - 1)/z]] == Sqrt[-(1/z)] Sqrt[z] (Pi/2 - ArcCos[1/Sqrt[z]])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], "z"]], "]"]], "\[Equal]", RowBox[List[SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", SqrtBox["z"], RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", " ", RowBox[List["ArcCos", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], ")"]]]]]]]]

 MathML Form

 cosh - 1 ( z - 1 z ) - 1 z z ( π 2 - cos - 1 ( 1 z ) ) z -1 z -1 1 2 -1 1 z -1 1 2 z 1 2 2 -1 -1 1 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcCos", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], ")"]]]]]]]]

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

 2003-08-21