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 ArcCosh

 http://functions.wolfram.com/01.26.27.1658.01

 Input Form

 ArcCosh[(1 + z)/(1 - z)] == (1 - Sqrt[1 - z] Sqrt[1/(1 - z)]) Pi I + 2 ArcTanh[Sqrt[z]]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21