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 ArcCosh

 http://functions.wolfram.com/01.26.16.0048.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21