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 ArcCoth

 http://functions.wolfram.com/01.28.27.2569.01

 Input Form

 ArcCoth[Sqrt[(z + 1)/(z - 1)]] == (-(1/2)) ArcCosh[z] /; Element[z, Reals] && -1 < z < 1

 Standard Form

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

 MathML Form

 coth - 1 ( z + 1 z - 1 ) - 1 2 cosh - 1 ( z ) /; ( z - 1 < z < 1 ) Condition z 1 z -1 -1 1 2 -1 1 2 z z -1 z 1 [/itex]

 Rule Form

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

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

 2003-09-04