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 ArcCosh

 http://functions.wolfram.com/01.26.27.1651.01

 Input Form

 ArcCosh[(z - 1)/(z + 1)] == -2 ArcTanh[1/Sqrt[-z]] /; Element[z, Reals] && z > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", ">", "0"]]]], ")"]]]]]]

 MathML Form

 cosh - 1 ( z - 1 z + 1 ) - 2 tanh - 1 ( 1 - z ) /; ( z z > 0 ) Condition z -1 z 1 -1 -2 1 -1 z 1 2 -1 z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["z_", "-", "1"]], RowBox[List["z_", "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", ">", "0"]]]]]]]]]]

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

 2003-08-21