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 ArcCoth

 http://functions.wolfram.com/01.28.27.2570.01

 Input Form

 ArcCoth[Sqrt[(z + 1)/(z - 1)]] == (1/2) ArcCosh[z] - Pi I /; Element[z, Reals] && 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["\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

 coth - 1 ( z + 1 z - 1 ) 1 2 cosh - 1 ( z ) - π /; ( z z < - 1 ) Condition z 1 z -1 -1 1 2 1 2 z -1 z 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["\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2003-09-04