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 ArcCosh

 http://functions.wolfram.com/01.26.27.0284.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21