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 ArcCosh

 http://functions.wolfram.com/01.26.27.1685.01

 Input Form

 ArcCosh[(1 + z^2)/(1 - z^2)] == (-Pi) I - 2 ArcTanh[1/z] /; Pi/2 < Arg[z] < Pi

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21