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 ArcCosh

 http://functions.wolfram.com/01.26.27.0562.01

 Input Form

 ArcCosh[(z^2 - 1)/(z^2 + 1)] == Pi I - 2 I ArcTan[z] /; 0 <= Arg[z] <= Pi/2

 Standard Form

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

 MathML Form

 cosh - 1 ( z 2 - 1 z 2 + 1 ) π - 2 tan - 1 ( z ) /; 0 arg ( z ) π 2 Condition z 2 -1 z 2 1 -1 -1 2 z 0 z 2 -1 [/itex]

 Rule Form

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

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

 2003-08-21